Difference between revisions of "Math 112 Calculus Learning Goals"

Latest revision as of 22:21, 15 November 2009

Chapter 1

Section 1.1

Homework:
Written: 25, 31, 40, 43, 55, 56, 64, 65
Online: o1 - o10

Goals:

Given a function described algebraically, find the
- domain 31, o4, o5
- range,
- value at a given number o2, o7
- value when we plug in another function, e.g. difference quotient 25, o2, o3.
Convert one representation of a function to another.
- verbal to/from graphical. o1
-algebraic to/from graphical. o6
-verbal to/from algebraic 55, 56, o9, o10
Piecewise functions: Given an algebraic description of a piecewise function, find its domain and sketch its graph. 43.
Be able to write the absolute value as a piecewise function, and use this to sketch its graph. 40, o6.
Use the definition of an even/odd function to decide whether a function described algebraically is even or odd. 65, o8
Use symmetry to decide whether a graph is an even or odd function. 64

Section 1.2

Homework:
Written: 4, 5, 7, 9, 12 and Appdx D: 24, 37*, 46
Online: o1 - o7

Goals

Write down a linear function given a set of information. 5, 12, o3, o4.
Recognize what the graph of linear, polynomial, power, trig, exponential, and log functions graph should look like. 4,7,o1
Given roots of a polynomial and one other point, write down its equation. 9, o2.
Know trig goals below. Appdx D:24, 37, 46, o5, o6, o7.

Trig to know, including problems to skim for practice.

Given angles in degrees and radians, draw the angle, convert from radians to degrees and vice versa. (See appendix D: 1-12)
Write down sin, cos, tan, sec, scs, cot of any angle 0, pi/6, pi/4, pi/3, pi/2, and all angles obtained from these angles by adding a multiple of pi/2. (appendix D:23-28)
Given a right triangle with side measurements, write sin, cos, tan, sec, csc, cot of any of the angles of the triangle in terms of the side lengths. (Appendix D: 35-38)
Similarly, given one trig ratio, find the others. (Appendix D: 29-34)
Graph trig functions. (app D: 77-82)
Use trig identities to simplify expressions (appendix D: 43-57 odd, 59-63), and to solve equations and inequalities involving trig functions (app D: 65-76).
- sin^2(x) + cos^2(x) = 1
- sin(-x) = -sin(x), cos(-x) = cos(x)
- sin(x+y) = sin(x)cos(y) + cos(x)sin(y), cos(x+y) = cos(x)cos(y) - sin(x)sin(y)
- 1+tan^2(x)=sec^2(x); 1+cot^2(x) = csc^2(x)
- sin(x-y), cos(x-y)
- sin(2x)
- cos(2x)

Section 1.3

Homework:
Written: 1, 7, 13, 17, 22, 39, 46, 60, 65
Online: o1 - o10

Goals

Apply and recognize transformations of functions:
- Given a graph, find an algebraic function. 1, 7, o1, o5, o9
- Given a formula, find a graph. 13, 14, 22, o6, o7
Given functions f and g, find: f+g, f-g, fg, f/g, and their domains. o2, o8.
Understand and apply compositions of functions:
- Given functions f and g, find g o f and f o g. 28, 39, 60, o3, o10
- Given f o g, find functions f and g. 46, 65, o4

Section 1.5

Homework:
Written: 11, 15, 18, 19, 21, 25, 29
Online: o1 - o5

Goals

Graph exponential functions a^x for a<1, a>1, as well as transformations of exponential functions from section 1.3. Find domains. 11, 15, 21, o1, o2
Given two points that an exponential function passes through, find the equation of the exponential function. 18, o3.
Use laws of exponents to simplify exponential expressions, to show various facts about exponential functions. 19, 29.
Convert a word problem involving population change into an algebraic expression involving exponential functions. Use this to find sizes of populations at given times, and to graph. 25, o4, o5.

Section 1.6

Homework:
Written: 12,16,18,19,23,35,45,48,54,60,67,71,73
Online: o1 - o14

Goals

Tell if a function is one-to-one when it is described
-algebraically 12
-graphically o1
Know the definition of an inverse function, and use it to find the value of the inverse function at a point 16, 18, o2, o6
Given a function, find its inverse
-algebraically 19,23,54,o3,o4,o5
-graphically 45,73,o7
Know the laws of logarithms and be able to solve and simplify logarithmic and exponential expressions. 35,48,o6,o8,o9,o10,o11
Know the inverses of the trigonometric functions
- domain and range 71
- values at a point 60, o12, o13
- simplify a trig function composed with an inverse trig function 67, o14

Chapter 2

Section 2.1

Homework:
Written: 4*, 5* (require calculator)

Goals

Know definitions of tangent and secant line. Compute the slope of a secant line. 4
Know definition of average velocity and the idea of instantaneous velocity. Compute an average velocity. 5
Explain how average velocity is equivalent to slope of a secant line, same for instantaneous velocity and slope of tangent line.

Section 2.2

Homework:
Written: 6, 7, 9, 16, 27, 32, 34a, 40
Online: o1 - o6

Goals

Idea of a limit: (Note: the "definition" of a limit in this section is sloppy and is not a real definition of a limit. See section 2.4)
- Find the limit of a function at a point from its graph, including when the limit does not exist. 6,7, o1, o2, o3
- Recognize the difference between the limit of a function at a point and the value of the function at a point. 6, 7, o1
- Give examples of functions that have prescribed limits at certain points. 16
- Understand that calculators and tables can entice you to guess a wrong limit. Give examples of functions whose limit is not what you would guess from plugging in values to your calculator. (no problems)
Idea (and notation) for one-sided limit: Do the same things for one-sided limits as done before for regular limits. 6, 7, o1, o2, o3, o4, o5, o6
Explain how one-sided and two-sided limits are connected. Use this to compute limits. 6, 7, o1, o2, o3
Infinite limits:
- Explain why infinity is not a number and how the definition of an infinite limit gets around this.
- Find all vertical asymptotes for a function. 9, 34a
- For rational functions, find when a limit is infinity and when it is negative infinity. 27, 32, 40, o4, o5, o6

Section 2.3a

Homework:
Written: 10,15,19,20,21,22,28,29
Online: o1 - o11

Goals

Apply limit laws to simplify limits
- algebraically o1
- graphically o2
Recognize when you can directly substitute to compute a limit and when you cannot. 10, o3, o4, o5, o6
Use algebra to simply and find limits.
- for polynomials over polynomials. 15, 19, 20, o4, o5, o6, o7, o8, o9
- expressions with square roots. 21, 22, 29, o10
- expressions with multiple fractions. 28, 29, o11

Section 2.3b

Homework:
Written: 36-39, 42, 55, 56, 58
Online: o1 - o8

Goals

Use the Squeeze Theorem to find limits. 36, 37, 38, o4, o5, o6
Evaluate limits that involve absolute values and other piecewise functions. 39, 42, o1, o2, o3
Use limit laws to find lim f(x) given that lim g(f(x)) = L. 55, 56, 58
Use substitution to rewrite lim g(f(x)) as lim g(u). o7, o8

Section 2.4

Homework:
Written: 2, 14, 15, 16, 19, 20, 23, 24
Online: o1 - o5

Goals:

Use a graph showing a function and lines y=L+epsilon, y=L-epsilon to find the largest value of delta so that if 0<|x-a|<delta, then |f(x)-L|<epsilon. 2
Know the epsilon-delta definition of a limit. Given a limit and a value for epsilon, be able to find the largest value of delta corresponding to that epsilon. 14, o1, o2, o3, o4, o5
Use the epsilon-delta definition of a limit to prove a statement about the limit of a linear function. 15, 16, 19, 20, 23, 24

Section 2.5a

Homework:
Written: 4, 6, 15, 18, 22, 23, 43ab, 58
Online: o1 - o9

Goals

Know the definition of continuity. Use it to determine why a given function is discontinuous, or limits and values of continuous functions. o1, o2, o3, o4
Given the graph of a function, be able to tell:
-where it is continuous. 4, o8
-where it is discontinuous, and the type of discontinuity. 6, o9
Given a function described algebraically, be able to tell:
-where it is continuous. 22, 23, o5, o6, o7
-where it is discontinuous and types of discontinuities. 15, 18, 43(a,b)
Use limit laws and the definition of continuity to prove facts about continuity (e.g. Theorem 4). 58

Section 2.5b

Homework:
Written: 28, 31, 32, 36, 37, 39, 41, 45, 47, 49, 65
Online: o1 - o7

Goals

Use continuity to evaluate limits 31, 32, o7
Continuity of piecewise functions
-determine if a piecewise function is continuous (or continuous from the right/left) 36,37,39
-determine parameters to make a piecewise function continuous 41,o1,o2,o3
Given a composition of functions, tell where it is continuous/discontinuous. 28
Use the Intermediate Value Theorem to prove the existence of solutions to equations. 45,47,49,65
Find intervals where a continuous function is positive/negative. o4, o5, o6

Section 2.6

Homework:
Written: 4, 5, 7, 13, 23, 24, 33, 43, 48
Online: o1 - o 14

Goals

Find the limit as x approaches +/-infinity, and equations of any horizontal asymptotes
-For a rational function, 13, 43, o1, o2, o6, o9, o11, o12, o13
-For a function described graphically, 4, o14
-For a function with exponentials in the numerator and denominator, 33, o7, o8
-For a function with square roots in the numerator and denominator. Be able to approach both infinity and negative infinity correctly in this case. 23, 24, o3, o4, o12
-Using the squeeze theorem. o10
Give examples of functions with prescribed horizontal and vertical asymptotes. 5, 7, 48

Section 2.7

Homework:
Written: 5, 9, 19, 20, 43, 44, 46
Online: o1 - o9

Goals

Given an algebraic function, take the derivative (using the definition of the derivative). Write down an equation for a tangent line through a point on a graph. 5, o4, o5, o8, o9
Given a word problem, interpret instantaneous or average rate of change. 43, 44, 46
Given a position function, find average and instantaneous velocity. o1, o2, o3
Sketch the graph of a function with prescribed derivatives. 19, 20
Given a limit expression, write down the point and function whose derivative it represents. o6, o7
Write both formal definitions of a derivative. Explain how the derivative can be interpreted as slope of a line, velocity, instantaneous change.

Section 2.8

Homework:
Written: 1, 3, 5, 6, 7, 9, 11, 19, 20, 25, 35, 36, 37, 38, 44, Prove that if a function f is differentiable at a, then f is continuous at a.
Online: o1 - o8

Goals

Given a function f, find a formula for the derivative of f using f'(x) = lim (h->0) [f(x+h)-f(x)]/h, and be able to state the domain of f'(x). 19, 20, 25, o7, o8
Given a graph of a function f, be able to find the graph of the first and second derivatives of f. Given a graph of the first and second derivatives of f, be able to find the graph of f. 1, 3, 5, 6, 7, 9, 11, o1, o4, o5, o6
Recognize when and why a function fails to be differentiable: 35, 36, 37, 38
a) corner
b) discontinuity (Theorem 4)
c) vertical tangent line
Be able to compute and apply higher derivatives: 44
- (f')'=f
- position [s(t)], velocity [v(t)=s'(t)], acceleration [a(t)=v'(t)=s''(t)]
Prove that if f is differentiable at a, then f is continuous at a. [Written homework]

Chapter 3

Section 3.1

Homework:
Written: 2, 13, 17, 20, 25, 28, 29, 33, 55, 61, 77
Online: o1 - o12

Goals

Compute derivatives using:
- The power rule. Especially, be able to rewrite functions so the power rule can be applied. 13, 17, 20, 25, 28, 29, all online problems.
- The derivative of e^x. 2, 17, 28, o12
- Sums, differences, and scalar multiples of functions you can differentiate with these rules. (almost all problems)
Use the definition of the derivative and limit laws to:
- Prove simple rules, including the power rule for n=-2, -1, -1/2, 1/2, 1, 2, as well as sum and difference rules. 61
- Compute certain limits. 77
Find a tangent line to the graph of a function at a given point. 33, 55, o2, o4, o5

Section 3.2

Homework:
Written: 2,11,13,23,24,32,33,47,49,55,57
Online: o1 - o11

Goals

Apply the product rule to find the derivative of functions. 11,24,33,47,49,55,57, o2,o4,o5,o6,o7
Apply the quotient rule to find the derivative of functions. 2,13,23,24,32,47,49 ,o3,o8,o10,o11
Be able to prove the product and quotient rules and variations. 55,57*

Section 3.3

Homework:
Written: 9, 10, 18, 20, 35, 42, 45, 49
Online: o1 - o15

Goals

Know derivatives for the 6 basic trig functions. Combine these with other differentiation rules to take derivatives. 9, 10, 18, 35, 49, o1, o2, o4, o8, o9, o10, o11, o12, o13, o14, o15
Know limits [2] and [3] in the book. Be able to use these to solve other limits involving trig functions. 42, 45, o5, o6, o7
Know the "periodicity" of differentiation of trig functions--i.e. the fourth derivative of the sine function is again the sine function. o3
Use the definition of the derivative plus the limits [2] and [3] to prove that the derivative of sin(x) is cos(x), and to prove that the derivative of cos(x) is -sin(x). 20

Section 3.4

Homework:
Written: 7, 24, 25, 31, 37, 47, 63, 65, 71, 84, 89
Online: o1 - o 14

Goals

Fluency in chain rule: Given a composition of functions, use the chain rule and other rules to compute its derivative quickly. 7, 25, 37, 47, o1, o2, o3, o4, o5, o6, o7, o8, o9, o10, o11
Given values of two functions and their derivatives at certain points, use the formal statement of the chain rule to compute the derivative of compositions of these functions. 63, 65, 71, o12, o13
Given a word problem involving the composition of functions, compute rates of change. Interpret the meaning of the derivative as a particular rate of change. 84, o14
Use the chain rule and definition of even/odd functions to prove properties of derivatives of even/odd functions. 89
Compute the derivative of a^x. 24, 31

Section 3.5

Homework:
Written: 3, 11, 12, 15, 18, 21, 23, 34, 41, 43, 57, 67
Online: o1 - o13

Goals

For an implicitly defined equation, use implicit differentiation to find
- dy/dx. 3, 11, 12, 15, 18, 21, o1, o2, o8, o10, o12
- dx/dy. 23
- d^2y/dx^2. 34, o7
Find the tangent line to an implicitly defined function. 41, 43, o3, o9, o11, o13
Use implicit differentiation to prove formulas for inverse functions, including inverse trig functions. 57, 67
Use formulas for derivatives of inverse trig functions, as well as other differentiation rules, to compute derivatives. o4, o5, o6

Section 3.6

Homework:
Written: 15, 17, 24, 27, 33, 39, 44, 48, 51, 54
Online: o1 - o14

Goals

Use formulas for the derivative of log_a(x) and ln(x), along with other differentiation rules, to compute derivatives. 15, 17, 24, 27, 33, 51, o1, o2, o3, o7, o8, o12, o14
Use logarithmic differentiation and/or properties of logs to simplify and then differentiate. Recognize which functions require logarithmic differentiation, and which derivatives become more convenient using logarithmic differentiation. 39, 44, 48, o4, o5, o6, o9, o10, o13
Know the formula for the number e as a limit. Use it to compute other limits involving e. 54

Section 3.8

Homework:
Written: 14, 15
Online: o1 - o7

Goals

Population growth. o1, o3, o4
Radioactive decay. Especially, know how to find half-life, or given half-life, find an equation. o5, o6
Cooling. 14, 15
Interest. o2, o7
- Derive the formula for compounding interest in n periods (see section 1.3, number 60)
- Use expression of e as a limit to find formula for continuously compounded interest. (In text, p 239)

Section 3.9

Homework:
Written: 5, 22, 33, 35, 37, 42
Online: o1 - o6

Goals

Solve related rates problems. (all homework problems)
a) Draw picture
b) Recognize variables from the problem, and rates of change as their derivatives.
c) Write equations relating variables (using geometry, trigonometry).
d) Differentiate, remembering to use the chain rule.
e) Plug in specific values to determine the requested answer.

Section 3.10

Homework:
Written: 1,2,3,5,23,28,43,44
Online: o1 - o4
(Merge both written and online with 3.11)

Goals

Compute the linearization of a function at a point. 1, 2, 3, 5, o1, o2
- Explain the relationship between the linearization and the tangent line. 5, o2
- Explain how linearization is useful. 23, 28, o4
Use the linearization at a point x=a to approximate the value of a function f(a+epsilon). 23, 28, o2, o3, o4

Section 3.11

Homework:
Written: 3, 7, 9, 15, 23, 29a, 33
Online: o5 - o7 (with section 3.10)

Goals

Know and be able to apply definitions of cosh and sinh to:
- Evaluate hyperbolic expressions at a point 3
- Prove cosh and sinh identities 7, 9, 15
- Find limits 23
- Prove the formulas for derivatives of hyperbolic functions. 24
Prove the formulas for the derivatives of cosh^-1, and sinh^-1. 29a.
Use the formulas for derivatives of sinh, cosh, sinh^-1, cosh^-1 to compute derivatives. 33, o5, o6, o7

Chapter 4

Section 4.1

Homework:
Written: 3, 7, 9, 10, 11, 13, 35, 40, 57, 60, 74, 76, 77
Online: o1 - o8

Goals

Given a graph, identify locations of absolute and local max's and min's, and absolute and local max/min values. Conversely, given information about absolute and local max/min, sketch an example of a graph. 3, 7, 9, 10, 11, 13
Find all critical numbers of a given function. 35, 40, o7, o8
Find absolute max/min values, and the points at which they occur, for a given function on a given interval. 57, 60, o1, o2, o3, o4, o5, o6,
Using the definition of local max/min, prove various statements about max/min's. 74, 76, 77

Section 4.2

Homework:
Written: 7, 15, 17, 28, 29, 30, 35
Online: o1 - o7

Goals

Know the statement of Rolle's theorem. In particular, given a function, show that it satisfies (or does not satisfy) all conditions of Rolle's theorem, then find the numbers that satisfy the conclusion of Rolle's theorem. o3, o4, o5
Know the statement of the Mean Value theorem. Given a function, show that it satisfies (or does not satisfy) all conditions of the Mean Value theorem, and then find the numbers that satisfy the conclusion of the Mean Value Theorem. 7, 15, o1, o2, o6
Use Rolle's theorem and the Mean Value theorem to show various facts:
- Show that an equation has at least one/ exactly one root. 17
- Given particular functions, prove there exist points where the derivative satisfies required properties. 28, 35
- Given restrictions on the derivative of a function, prove the function satisfies certain properties. 29, o7, proof of Theorem 5 page 284, proof of Corollary 7 page 284
Use corollary 7 to prove certain functions differ by a constant. 30

Section 4.3

Homework:
Written: 1, 6, 7, 21, 23, 25, 28, 31, 72
Online: o1 - o4

Goals

Know and apply the increasing/decreasing test to determine where a function f is increasing/decreasing
- Given a graph of f, f', or f. 1, 6, 31, o4
- Given an algebraic expression for f. o1, o3
Find local maxima and minima using first and second derivative tests
- Given a graph for f'. 6, 31, o4
- Given an algebraic expression for f. 21
- Given information about values of f' and f at a point. 23
Know the definition of concavity and how to determine concavity (the concavity test). 31, 72, o2, o3, o4
Know the definition of a point of inflection and how to find it. 7, 31, o4
Know how the above information affects the graph of a function. Given intervals where first and second derivatives are positive and negative, sketch a graph. 25, 28

Section 4.4

Homework:
Written: 4, 7, 15, 31, 33, 39, 47, 49, 57, 70, 71, 81
Online: o1 - o10

Goals

Know when to use L'Hospital's rule to solve a limit. (All problems, particularly 4, 71, others)
Use L'Hospital's rule to find limits of functions of the following indeterminate forms:
- infinity/infinity or 0/0. 7, 15, 33, 70, 81, o1, o3, o6
- Indeterminate products. 39, 08
- Indeterminate differences. 47, 49, o4, o7
- Indeterminate powers. 57, o9, o10

Section 4.5

Homework:
Written: 5, 12, 32, 47, 49
Online: o1 - o2

Goals

Use all of the following to draw graphs of functions: (all problems)
* Algebraic Properties (Domain, intercepts, even/odd/periodic)
* Limit Properties (Asymptotes, singularities, discontinuities)
* Derivative Properties (Increasing/decreasing, extrema, concavity/inflection)

Section 4.7

Homework:
Written: 7, 14, 31, 35, 41, 47, 66
Online: o1 - o6

Goals

Convert word problems into formulas, and use methods for finding extreme values to solve optimization problems. Interpret your answer in terms of the original problem. Types of problems:
- Given a formula relating two quantities. 7, 41, o2
- 2-dimensional geometric objects, including rectangles, triangles, circles. (Know areas, similar triangle facts) 31, 47, 66, o1, o3, o5
- 3-dimensional geometric objects, including rectangular boxes, cylinders, spheres, cones. (Know volume, surface area) 14, 35, o4, o6

Section 4.8

Homework:
Written: 1, 2, 3, 4, 29
Online: o1 - o3

Goals

Use Newton's Method to approximate roots/solutions of equations. 1, 2, 3, 4, 29, o1, o2, o3
Derive the formula for Newton's Method from the tangent line equation.
Give an example of a function 'f' and a starting point 'x_1' that makes Newton's Method fail. 4, o3

Section 4.9

Homework:
Written: 12, 15, 20, 27, 33, 49, 51, 53, 67, 69, 74
Online: o1 - o10

Goals

Use the Mean value Theorem to prove Theorem 1.
Memorize the table of anti-differentiation formulas on page 341 and relate it to the table of derivatives on the inside back cover of the book.
- Use these formulas and Theorem 1 to find *all* antiderivatives of various functions. 12, 15, 20, 27, o5, o6, o7
- Use these formulas and Theorem 1 to find a unique anti-derivative with given values at specified points. 33, 51, 53, 67, 69, 70, 74, o1, o2, o3, o4, o8, o9, o10
Use anti-differentiation to solve physical and economic problems, especially problems of motion. 67, 69, 70, 74, o3, o4

Chapter 5

Appendix E

Homework:
Written: 1, 3, 5, 10, 11, 15, 17, 20, 23, 41, 43
Online: o1 - o9

Goals

Write expanded sums in sigma notation, 1, 3, 5, 10
and expand sums written in sigma notation. 11, 15, 17, 20).
Numerically evaluate sums. 23
Apply appropriate rules to distribute constants or expand sums of sums. o3, o4, o6.
Explicitly evaluate a sum (in sigma notation) in terms of 'n', where the summand is a polynomial in x of degree at most 3. Degree 0: o5; degree 1: o1, o2; degree 2: o3, o4; degree 3: o5
Evaluate telescoping sums. 41
Evaluate limits of sums. 43, 06
Change the index of summation. o7, o8, o9

Section 5.1/5.2a

Homework:
Written: 5.1: 1a, 12, 18, 21, 26; 5.2: 5ab, 17, 29, 30, 70
Online: o1 - o5

Goals

Use left and right sums to approximate area under a continuous function. 5.1: 1a, o1
Use the definitions of area under the curve to write the area as a limit. Use the definition of integral to write the integral as a limit. Conversely, given a limit that represents the area under a curve or an integral, find the region whose area is given, or write the integral. 5.1: 18, 21; 5.2: 17, 29, 30, 70; o4, o5.
Approximate integrals by left and right sums. 5.2: 5ab, o3.
Calculate a net change. Interpret total change problems as area problems. 5.1: 12, o2

Section 5.2

Homework:
Written: 34, 37, 43, 47, 49, 50, 55, 63
Online: o1 - o8

Goals

Evaluate a given integral by interpreting it in terms of area. 34, 37, o1, o2, o3, o4
Use properties of the definite integral to
- Rewrite integrals 47, 50, o5
- Evaluate integrals 43, 49, o6
- Estimate integrals 55, o7, o8
Use the definition of the definite integral to prove properties of the definite integral. 63

Section 5.3a

Homework:
Written: 9, 15, 56, 57, 63, 64
Online: o1 - o8

Goals

Understand and explain the relationship between area and derivative described by the Fundamental Theorem.
Describe properties of functions defined by integrals, including their values at particular points, intervals where they are increasing/decreasing, maxima and minima, etc. 3, o7, 63, 64
Differentiate functions defined by integrals 9, 15, 56, 57, o1, o2, o3, o4, o5, o6, o8

Section 5.3b

Homework:
Written: 22, 31, 36, 41, 43, 59, 65, 66, 74
Online: o1 - o10

Goals

Given a function and limits of integration verify that the hypotheses of the Fundamental Theorem hold. 43
Use the Fundamental Theorem to evaluate the definite integral of a function. 22, 31, 41, o1 - o10.
Given the definite integral of a function, use the Fundamental Theorem to determine information about the function, or limits of integration. 59, 74
Recognize a limit of Riemann sums as a definite integral, and evaluate that definite integral using the Fundamental Theorem. 65, 66

Section 5.4

Homework:
Written: 4, 9, 23, 32, 43, 49, 54, 59, 61, 65
Online: o1 - o10

Goals

Evaluate definite and indefinite integrals for all standard functions (polynomials 9, o1a, o3, o6a, o6c, rational functions 4, o1b, o1c, o4, o6b, o7, o8, trigonometric functions and inverses 32, o5, o8, o9abc, o10, exponentials 23, 32 and logarithms o8, absolute value 43, etc.)
Multiply, divide, substitute, or otherwise change the form of a function to make it easier to integrate.
Solve problems about net change by setting up and evaluating appropriate integrals of rates of change (density 61, marginal cost 65, displacement/distance o2, water flow o10, etc).

Section 5.5a

Homework:
Written: 5, 8, 9, 21, 25, 31, 38, 39
Online: o1 - o9

Goals

Use the substitution rule to evaluate indefinite integrals. (all problems)
- Become proficient in choosing a productive substitution. (all problems)
- Use substitution to simplify a problem by substituting for more than one function or variable. o5, o7

Section 5.5b

Homework:
Written: 45, 46, 53, 73, 83
Online: o1 - o10

Goals

Use the substitution rule to evaluate definite integrals. 53, o2, o3, o4, o5, o6, o7, o8, o9
Use substitution with other previously learned techniques to evaluate integrals, e.g. interpreting an integral as the area under a curve. 73
Use substitution to simplify a problem by substituting for more than one function or variable. 45, 46, o1, o4
The substitution rule "undoes" one of the differentiation rules you learned in chapter 3. Which rule? o10

@@ Line 1: / Line 1: @@
 ----
+== Chapter 1 ==
-== Section 1.1 ==
+=== Section 1.1 ===
 Homework: <br>
-Written: 25, 31, 40, 43, 44, 56, 64, 65<br>
+Written: 25, 31, 40, 43, 55, 56, 64, 65<br>
 Online: o1 - o10
@@ Line 27: / Line 28: @@
 ----
-== Section 1.2 ==
+=== Section 1.2 ===
 Homework:<br>
@@ Line 42: / Line 43: @@
-== Trig to know, including problems to skim for practice. ==
+=== Trig to know, including problems to skim for practice. ===
-. Given angles in degrees and radians, draw the angle, convert from radians to degrees and vice versa. (See appendix D: 1-12)
+<ol>
-. Write down sin, cos, tan, sec, scs, cot of any angle 0, pi/6, pi/4, pi/3, pi/2, and all angles obtained from these angles by adding a multiple of pi/2. (appendix D:23-28)
+<li> Given angles in degrees and radians, draw the angle, convert from radians to degrees and vice versa. (See appendix D: 1-12)
-. Given a right triangle with side measurements, write sin, cos, tan, sec, csc, cot of any of the angles of the triangle in terms of the side lengths. (Appendix D: 35-38)
+<li> Write down sin, cos, tan, sec, scs, cot of any angle 0, pi/6, pi/4, pi/3, pi/2, and all angles obtained from these angles by adding a multiple of pi/2. (appendix D:23-28)
+<li> Given a right triangle with side measurements, write sin, cos, tan, sec, csc, cot of any of the angles of the triangle in terms of the side lengths. (Appendix D: 35-38)<br>
        Similarly, given one trig ratio, find the others. (Appendix D: 29-34)
-. Graph trig functions. (app D: 77-82)
+<li> Graph trig functions. (app D: 77-82)
-. Use trig identities to simplify expressions (appendix D: 43-57 odd, 59-63), and to solve equations and inequalities involving trig functions (app D: 65-76).
+<li> Use trig identities to simplify expressions (appendix D: 43-57 odd, 59-63), and to solve equations and inequalities involving trig functions (app D: 65-76).<br>
-          * Most important identities: sin^2(x) + cos^2(x) = 1
+<ul>Most important identities:
-          * sin(-x) = -sin(x)
+    <li> sin^2(x) + cos^2(x) = 1
-          * cos(-x) = cos(x)
+    <li> sin(-x) = -sin(x), cos(-x) = cos(x)
-          * sin(x+y) = sin(x)cos(y) + cos(x)sin(y)
+    <li> sin(x+y) = sin(x)cos(y) + cos(x)sin(y), cos(x+y) = cos(x)cos(y) - sin(x)sin(y)
-          * cos(x+y) = cos(x)cos(y) - sin(x)sin(y)
+</ul>
-      Using the above, you can derive other identities:
+<ul> Using the above, derive other identities:
-          * 1+tan^2(x)=sec^2(x); 1+cot^2(x) = csc^2(x)
+    <li> 1+tan^2(x)=sec^2(x); 1+cot^2(x) = csc^2(x)
-          * sin(x-y)
+    <li> sin(x-y), cos(x-y)
-          * cos(x-y)
+    <li> sin(2x)
-          * sin(2x)
+    <li> cos(2x)
-          * cos(2x)
+</ul>
+</ol>
 ----
-== Section 1.3 (Savannah) ==
+=== Section 1.3 ===
-Homework
+Homework:<br>
+Written: 1, 7, 13, 17, 22, 39, 46, 60, 65<br>
+Online: o1 - o10
-    Written: 1,7,13, 14, 22, 39, 46, 60, 65
+'''Goals'''
-    Online: Modify 1 to be y as a function of x. Replace 6 with a different word problem. Add 3 from section 1.2 online assignment.
+<ol>
+<li> Apply and recognize transformations of functions:<br>
-Goals
+   - Given a graph, find an algebraic function. 1, 7, o1, o5, o9<br>
+   - Given a formula, find a graph.  13, 14, 22, o6, o7
-. Apply and recognize transformations of functions:
+<li> Given functions f and g, find: f+g, f-g, fg, f/g, and their domains.  o2, o8.
-      - Translating, Stretching, Reflecting, Absolute Value  1
+<li> Understand and apply compositions of functions:<br>
-      - Graph --> Algebraic  7, O1, O5, 1.2-O3
+       - Given functions f and g, find g o f and f o g.  28, 39, 60, o3, o10<br>
-      - Algebraic --> Graph  13, 14, 22, O7, O8
+       - Given f o g, find functions f and g.  46, 65, o4
-. Given functions f and g, find:
+</ol>
-      - f+g
-      - f-g
-      - fg
-      - f/g
-      - domains for above functions.   O2, O9
-. Understand and apply compositions of functions:
-       - Given functions f and g, find g o f and f o g.  28, 39, 60, O3, O6
-       - Given f o g, find functions f and g.  46, 65, O4
 ----
-== Section 1.5 (James) ==
+=== Section 1.5 ===
-Homework:
+Homework: <br>
+Written: 11, 15, 18, 19, 21, 25, 29<br>
+Online:  o1 - o5
-  Written: 11, 15, 18, 19, 21, 25, 29
+'''Goals'''
-  Online:  o2, o3, o4, o5, one more word problem
+<ol>
+<li>  Graph exponential functions a^x for a<1, a>1, as well as transformations of exponential functions from section 1.3.  Find domains.  11, 15, 21, o1, o2
+<li>  Given two points that an exponential function passes through, find the equation of the exponential function.  18, o3.
+<li>  Use laws of exponents to simplify exponential expressions, to show various facts about exponential functions. 19, 29.
+<li> Convert a word problem involving population change into an algebraic expression involving exponential functions.  Use this to find sizes of populations at given times, and to graph.  25, o4, o5.
+</ol>
-Goals
-.  Graph exponential functions a^x for a<1, a>1, as well as transformations of exponential functions from section 1.3.  Find domains.  11, 15, 21, o2
-.  Given two points that an exponential function passes through, find the equation of the exponential function.  18, o3.
-.  Use laws of exponents to simplify exponential expressions, to show various facts about exponential functions. 19, 29.
-.  Convert a word problem involving population change into an algebraic expression involving exponential functions.  Use this to find sizes of populations at given times, and to graph.  25, o4, o5.
+----
+=== Section 1.6 ===
+Homework:<br>
+Written: 12,16,18,19,23,35,45,48,54,60,67,71,73<br>
+Online: o1 - o14
+'''Goals'''
+<ol>
+<li> Tell if a function is one-to-one when it is described<br>
+ -algebraically 12<br>
+ -graphically  o1
+<li> Know the definition of an inverse function, and use it to find the value of the inverse function at a point 16, 18, o2, o6
+<li> Given a function, find its inverse<br>
+  -algebraically 19,23,54,o3,o4,o5<br>
+  -graphically 45,73,o7
+<li> Know the laws of logarithms and be able to solve and simplify logarithmic and exponential expressions. 35,48,o6,o8,o9,o10,o11
+<li> Know the inverses of the trigonometric functions <br>
+      - domain and range  71<br>
+      - values at a point 60, o12, o13 <br>
+      - simplify a trig function composed with an inverse trig function 67, o14
+</ol>
 ----
+== Chapter 2 ==
-== Section 1.6 (McKay) ==
+=== Section 2.1 ===
-Homework
+Homework:<br>
+Written: 4*, 5* (require calculator)
-   Written: 12,16,18,19,23,35,45,48,54,60,67,71,73
+'''Goals'''
-   Online: 01,02,03,04,05,06,07,08,010,011,012,013,016,018
+<ol>
+<li> Know definitions of tangent and secant line. Compute the slope of a secant line. 4
-Goals
+<li> Know definition of average velocity and the idea of instantaneous velocity. Compute an average velocity. 5
+<li>  Explain how average velocity is equivalent to slope of a secant line, same for instantaneous velocity and slope of tangent line.
-) Be able to tell if a function is one-to-one
+</ol>
-      -algebraically 12
-      -graphically  01
-) Know the definition of an inverse function and be able to use the steps to find the inverse
-      -algebraically 16,19,23,54,02,03,04,05,06
-      -graphically 18,45,73,07
-)Know the laws of logarithms and be able to solve and simplify logarithmic and exponential expressions. 35,48,06,08,010,011,012
-)Know the inverses of the trigonometric functions
-      - domain and range  71
-      - values at a point 60, 013,016
-      - simplify a trig function composed with an inverse trig function 67, o18
 ----
-== Section 2.1 (Tyler) ==
+=== Section 2.2 ===
-Homework
+Homework:<br>
+Written: 6, 7, 9, 16, 27, 32, 34a, 40<br>
+Online: o1 - o6
-    Written:4*, 5*? (require calculator)
-Goals
+'''Goals'''
+<ol>
-. Know definitions of tangent and secant line. Compute the slope of a secant line. 4
+<li> Idea of a limit: (Note: the "definition" of a limit in this section is sloppy and is not a real definition of a limit. See section 2.4)
-. Know definition of average velocity and the idea of instantaneous velocity. Compute an average velocity. 5
+ <ul>
-.  Explain how average velocity is equivalent to slope of a secant line, same for instantaneous velocity and slope of tangent line.
+     <li>Find the limit of a function at a point from its graph, including when the limit does not exist. 6,7, o1, o2, o3
+     <li> Recognize the difference between the limit of a function at a point and the value of the function at a point. 6, 7, o1
+     <li> Give examples of functions that have prescribed limits at certain points. 16
+     <li> Understand that calculators and tables can entice you to guess a wrong limit. Give examples of functions whose limit is not what you would guess from plugging in values to your calculator. (no problems)
+  </ul>
+<li> Idea (and notation) for one-sided limit: Do the same things for one-sided limits as done before for regular limits. 6, 7, o1, o2, o3, o4, o5, o6
+<li> Explain how one-sided and two-sided limits are connected. Use this to compute limits. 6, 7, o1, o2, o3
+<li> Infinite limits:
+  <ul>
+      <li> Explain why infinity is not a number and how the definition of an infinite limit gets around this.
+      <li> Find all vertical asymptotes for a function. 9, 34a
+      <li> For rational functions, find when a limit is infinity and when it is negative infinity. 27, 32, 40, o4, o5, o6
+  </ul>
+</ol>
 ----
-== Section 2.2 (Tyler) ==
+=== Section 2.3a ===
-Homework
+Homework:<br>
+Written: 10,15,19,20,21,22,28,29<br>
-    Written: 6, 7, 9, 16, 27, 32, 34a, 40
+Online: o1 - o11
-    Online: kill O2, O5. Modify: O3 fix so different parts don't have same answer.
-                  O6, O7, O8: Use the same input notation for infinity. O8 Delete irrelevant lecture about asymptotes.
-Goals:
-. Idea of a limit: (Note: the "definition" of a limit in this section is sloppy and is not a real definition of a limit. See section 2.4)
-          * Find the limit of a function at a point from its graph, including when the limit does not exist. 6,7, O1, O3
-          * Recognize the difference between the limit of a function at a point and the value of the function at a point. 6, 7, O1
-          * Give examples of functions that have prescribed limits at certain points. 16
-          * Understand that calculators and tables can entice you to guess a wrong limit. Give examples of functions whose limit is not what you would guess from plugging in values to your calculator. (no problems)
-. Idea (and notation) for one-sided limit: Do the same things for one-sided limits as done before for regular limits. 6, 7, O1, O3, O4, O6, O7, O8
-. Explain how one-sided and two-sided limits are connected. Use this to compute limits. 6, 7, O1, O3, O4, O6, O7, O8
-. Infinite limits:
-          * Explain why infinity is not a number and how the definition of an infinite limit gets around this.
-          * Find all vertical asymptotes for a function. 9, 34a
-          * For rational functions, find when a limit is infinity and when it is negative infinity. 27, 32, O6, O7, O8, 40
+'''Goals'''
+<ol>
+<li> Apply limit laws to simplify limits <br>
+         - algebraically  o1<br>
+         - graphically    o2
+<li> Recognize when you can directly substitute to compute a limit and when you cannot.  10, o3, o4, o5, o6
+<li> Use algebra to simply and find limits. <br>
+     - for polynomials over polynomials. 15, 19, 20, o4, o5, o6, o7, o8, o9<br>
+     - expressions with square roots. 21, 22, 29, o10<br>
+     - expressions with multiple fractions.  28, 29, o11
+</ol>
 ----
-== Section 2.3a (Rebecca) ==
+=== Section 2.3b ===
-Homework
+Homework:<br>
+Written: 36-39, 42, 55, 56, 58<br>
+Online: o1 - o8
-    Written: 10,15,19,20,21,22,28,29
+'''Goals'''
-    Online: Get rid of 3
+<ol>
+<li> Use the Squeeze Theorem to find limits.  36, 37, 38, o4, o5, o6
+<li> Evaluate limits that involve absolute values and other piecewise functions. 39, 42, o1, o2, o3
+<li> Use limit laws to find lim f(x) given that lim g(f(x)) = L. 55, 56, 58
+<li>  Use substitution to rewrite lim g(f(x)) as lim g(u).  o7, o8
+</ol>
-Goals
+----
-. Be able to apply limit laws to simplify limits
+=== Section 2.4 ===
-         - algebraically  01
+Homework:<br>
-         - graphically    02
+Written:  2, 14, 15, 16, 19, 20, 23, 24<br>
-. Recognize when you can directly substitute to compute a limit and when you cannot.  10, 03, 04, 05, 06
+Online:  o1 - o5
-. Use algebra to simply and find limits.
-     - for polynomials over polynomials. 15, 19, 20, o5, o6, o7, o8, o9, o10
+'''Goals:'''
-     - expressions with square roots. 21, 22, 29, o11
+<ol>
-     - expressions with multiple fractions.  28, 29, o12
+<li>  Use a graph showing a function and lines y=L+epsilon, y=L-epsilon to find the largest value of delta so that if 0<|x-a|<delta, then |f(x)-L|<epsilon.  2
+<li>  Know the epsilon-delta definition of a limit.  Given a limit and a value for epsilon, be able to find the largest value of delta corresponding to that epsilon.  14, o1, o2, o3, o4, o5
+<li>  Use the epsilon-delta definition of a limit to prove a statement about the limit of a linear function.  15, 16, 19, 20, 23, 24
+</ol>
 ----
-== Section 2.3b (Drew) ==
+=== Section 2.5a ===
+Homework:<br>
+Written: 4, 6, 15, 18, 22, 23, 43ab, 58<br>
+Online: o1 - o9
-Homework
-    Written: 36-39, 42, 55, 56, 58
+'''Goals'''
-    Online: Add o2 from 2.2.  Kill o3, o4.  Modify o6 so that direct substitution doesn't work.  Add two problems using substitution.
+<ol>
+<li> Know the definition of continuity.  Use it to determine why a given function is discontinuous, or limits and values of continuous functions.  o1, o2, o3, o4
+<li> Given the graph of a function, be able to tell:<br>
+   -where it is continuous.  4, o8<br>
+   -where it is discontinuous, and the type of discontinuity.  6, o9
+<li> Given a function described algebraically, be able to tell:<br>
+      -where it is continuous.  22, 23, o5, o6, o7<br>
+      -where it is discontinuous and types of discontinuities.  15, 18, 43(a,b)
+<li> Use limit laws and the definition of continuity to prove facts about continuity (e.g. Theorem 4). 58
+</ol>
-Goals
-. Use the Squeeze Theorem to find limits.  36, 37, 38, o5, o6, o7
-. Evaluate limits that involve absolute values and other piecewise functions. 39, 42, o1, o2, o2 from 2.2
-. Use limit laws to find lim f(x) given that lim g(f(x)) = L. 55, 56, 58
-.  Use substitution to rewrite lim g(f(x)) as lim g(u).  2 new online problems.
 ----
-== Section 2.4 (Jessica) ==
+=== Section 2.5b ===
-Homework:
-  Written:  2, 14, 15, 16, 19, 20
-  Online:  kill o6 (done), modify problems to find the *largest* delta (done).
-Goals:
+Homework:<br>
-.  Use a graph showing a function and lines y=L+epsilon, y=L-epsilon to find the largest value of delta so that if 0<|x-a|<delta, then |f(x)-L|<epsilon.  2
+Written: 28, 31, 32, 36, 37, 39, 41, 45, 47, 49, 65<br>
-.  Know the epsilon-delta definition of a limit.  Given a limit and a value for epsilon, be able to find the largest value of delta corresponding to that epsilon.  14, o1, o2, o3, o4, o5
+Online:  o1 - o7
-.  Use the epsilon-delta definition of a limit to prove a statement about the limit of a linear function.  15, 16, 19, 20.
+'''Goals'''
+<ol>
+<li> Use continuity to evaluate limits 31, 32, o7
+<li> Continuity of piecewise functions<br>
+      -determine if a piecewise function is continuous (or continuous from the right/left) 36,37,39 <br>
+      -determine parameters to make a piecewise function continuous 41,o1,o2,o3
+<li> Given a composition of functions, tell where it is continuous/discontinuous. 28
+<li> Use the Intermediate Value Theorem to prove the existence of solutions to equations. 45,47,49,65
+<li> Find intervals where a continuous function is positive/negative. o4, o5, o6
+</ol>
 ----
-== Section 2.5a (McKay/Savannah) ==
+=== Section 2.6 ===
+Homework:<br>
+Written:  4, 5, 7, 13, 23, 24, 33, 43, 48<br>
+Online: o1 - o 14
-    Written:4, 6, 15, 18, 22, 23, 43ab, 58
+'''Goals'''
-    Online - Kill O2-O4, O11-O16; Change O8, O9, O10 to ask, "Where is the following function continuous?"; Add a graph problem where the student must identify where the graph is discontinuous; Add a graph problem where the student must identify the types of discontinuities
+<ol>
+<li> Find the limit as x approaches +/-infinity, and equations of any horizontal asymptotes<br>
-. Given the graph of a function, be able to tell:
+  -For a rational function, 13, 43, o1, o2, o6, o9, o11, o12, o13<br>
-      a) where it is continuous.  4
+  -For a function described graphically, 4, o14<br>
-      b) where it is discontinuous, and the type of discontinuity.  6
+  -For a function with exponentials in the numerator and denominator, 33, o7, o8<br>
-. Given a function described algebraically, be able to tell:
+  -For a function with square roots in the numerator and denominator.  Be able to approach both infinity and negative infinity correctly in this case.  23, 24, o3, o4, o12<br>
-      a) where it is continuous.  22, 23, O1, O8, O9, O10
+  -Using the squeeze theorem. o10
-      b) where it is discontinuous and types of discontinuities.  15, 18, 43(a,b), O5, O6, O7
+<li> Give examples of functions with prescribed horizontal and vertical asymptotes.  5, 7, 48
-      This includes functions from Theorem 7, piecewise functions, and combinations of functions.
+</ol>
-. Use limit laws and the definition of continuity to prove facts about continuity (e.g. Theorem 4). 58
 ----
-== Section 2.5b (Mark) ==
+=== Section 2.7 ===
-Homework
+Homework:<br>
+Written:  5, 9, 19, 20, 43, 44, 46<br>
+Online:  o1 - o9
-    Written: 28, 31, 32, 36, 37, 39, 41, 45, 47, 49, 65
+'''Goals'''
-    Online: Kill 3, 5, 6, 7. Add 3 problems: Find intervals where f is positive, negative. One quadratic, easy factor; one rational with linear top and bottom; one rational with quadratic top, perfect square bottom.
+<ol>
+<li> Given an algebraic function, take the derivative (using the definition of the derivative).  Write down an equation for a tangent line through a point on a graph. 5, o4, o5, o8, o9
-Goals
+<li> Given a word problem, interpret instantaneous or average rate of change.  43, 44, 46<br>
+  Given a position function, find average and instantaneous velocity. o1, o2, o3
-. Use continuity to evaluate limits 31,32
+<li> Sketch the graph of a function with prescribed derivatives. 19, 20
-. Continuity of piecewise functions
+<li> Given a limit expression, write down the point and function whose derivative it represents. o6, o7
-      -determine if a piecewise function is continuous (or continuous from the right/left) 36,37,39
+<li> Write both formal definitions of a derivative. Explain how the derivative can be interpreted as slope of a line, velocity, instantaneous change.
-      -determine parameters to make a piecewise function continuous 41,O1,O2,O4
+</ol>
-. Given a composition of functions, tell where it is continuous/discontinuous. 28
-. Use the Intermediate Value Theorem to prove the existence of solutions to equations. 45,47,49,65
-. Find intervals where a continuous function is positive/negative. (3 new online problems)
 ----
-== Section 2.6 (Skyler) ==
+=== Section 2.8 ===
-Homework:
+Homework:<br>
-  Written:  4, 5, 7, 13, 33, 43, 48
+Written: 1, 3, 5, 6, 7, 9, 11, 19, 20, 25, 35, 36, 37, 38, 44, Prove that if a function f is differentiable at a, then f is continuous at a.<br>
-  Online: Drop #15
+Online: o1 - o8
-Goals
+'''Goals'''
+<ol>
-. Understand definition of limit at +/- inf
+<li> Given a function f, find a formula for the derivative of f using f'(x) = lim (h->0) [f(x+h)-f(x)]/h, and be able to state the domain of f'(x).  19, 20, 25, o7, o8
-. Find the limit of a rational function as x -> +/-inf and equations of horizontal asymptotes (when they exist)
+<li> Given a graph of a function f, be able to find the graph of the first and second derivatives of f. Given a graph of the first and second derivatives of f, be able to find the graph of f.  1, 3, 5, 6, 7, 9, 11, o1, o4, o5, o6
-. Identify functions whose limit at +/- inf does not exist or whose limit is infinite
+<li> Recognize when and why a function fails to be differentiable:  35, 36, 37, 38<br>
-. Compute limits at infinity by graphs and algebraic techniques
+      a) corner<br>
+      b) discontinuity (Theorem 4)<br>
+      c) vertical tangent line<br>
+<li> Be able to compute and apply higher derivatives:  44<br>
+      - (f')'=f''<br>
+      - position [s(t)], velocity [v(t)=s'(t)], acceleration [a(t)=v'(t)=s<nowiki>''</nowiki>(t)]
+<li> Prove that if f is differentiable at a, then f is continuous at a.  [Written homework]
+</ol>
 ----
-== Section 2.7 (Sam) ==
+== Chapter 3 ==
-Homework:
-  Written:  5,9,19, 20, 43,44, 46
-  Online:  eliminate o7,o9,o12
-Goals:
+=== Section 3.1  ===
-. Given an algebraic function, take the derivative (using the definition of the derivative)
-        Write down an equation for a tangent line through a point on a graph 3, 5, 05, o10, o11
-. Given a real life situation, interpret instantaneous change or average of change  43, 44, 46
-        Given a position function (or graph thereof), interpret the graph or find (average) velocity o1, o2, o3
-.  Sketch the graph of a function such that certain criteria are met (values at certain points, derivatives, etc.) 19, 20
-.  Given a limit expression, write down the point and function whose derivative it represents o6, o8
-.  Write both formal definitions of a derivative
-        Explain how the derivative can be interpreted as slope of a line, velocity, instantaneous change
+Homework:<br>
+Written:  2, 13, 17, 20, 25, 28, 29, 33, 55, 61, 77<br>
+Online:  o1 - o12
+'''Goals'''
+<ol>
+<li>  Compute derivatives using:
+  <ul>
+    <li>  The power rule.  Especially, be able to rewrite functions so the power rule can be applied.  13, 17, 20, 25, 28, 29, all online problems.
+    <li>  The derivative of e^x.  2, 17, 28, o12
+    <li>  Sums, differences, and scalar multiples of functions you can differentiate with these rules. (almost all problems)
+  </ul>
+<li>  Use the definition of the derivative and limit laws to:
+  <ul>
+    <li> Prove simple rules, including the power rule for n=-2, -1, -1/2, 1/2, 1, 2, as well as sum and difference rules.  61
+    <li> Compute certain limits.  77
+  </ul>
+<li>  Find a tangent line to the graph of a function at a given point.  33, 55, o2, o4, o5
+</ol>
-Changes:
- Added: 43, 44
- Eliminating:  2,25, o7, o9, o12
 ----
-== Section 2.8 (Savannah) ==
+=== Section 3.2 ===
-Homework
+Homework:<br>
+Written:  2,11,13,23,24,32,33,47,49,55,57<br>
+Online: o1 - o11
-    Written: 1, 3, 5, 6, 7, 9, 11, 19, 20, 25, 35, 36, 37, 38, 44, Prove that if a function f is differentiable at a, then f is continuous at a.
+'''Goals'''
-    Online: Kill O2, O3, Change O9 to f'(x)
+<ol>
+<li> Apply the product rule to find the derivative of functions. 11,24,33,47,49,55,57,  o2,o4,o5,o6,o7
+<li> Apply the quotient rule to find the derivative of functions. 2,13,23,24,32,47,49 ,o3,o8,o10,o11
+<li> Be able to prove the product and quotient rules and variations. 55,57*
+</ol>
-Goals
+----
-. Given a function f, find a formula for the derivative of f using f'(x) = lim (h->0) [f(x+h)-f(x)]/h, and be able to state the domain of f'(x).  19, 20, 25, O9, O10
+=== Section 3.3 ===
-. Given a graph of a function f, be able to find the graph of f', f''. Given a graph of a function f', f'', be able to find th graph of f.  1, 3, 5, 6, 7, 9, 11, O1, O4, O5
-. Recognize when and why a function fails to be differentiable:  35, 36, 37, 38
-      a) corner
-      b) discontinuity (Theorem 4)
-      c) vertical tangent line
-. Be able to compute and apply higher derivatives:  O6, O7, O8, 44
-      - (f')'=f''
-      - position [s(t)], velocity [v(t)=s'(t)], acceleration [a(t)=v'(t)=s''(t)]
-. Prove that if f is differentiable at a, then f is continuous at a.  [Written homework]
+Homework:<br>
+Written:  9, 10, 18, 20, 35, 42, 45, 49<br>
+Online: o1 - o15
+'''Goals'''
+<ol>
+<li> Know derivatives for the 6 basic trig functions.  Combine these with other differentiation rules to take derivatives.  9, 10, 18, 35, 49, o1, o2, o4, o8, o9, o10, o11, o12, o13, o14, o15
+<li> Know limits [2] and [3] in the book.  Be able to use these to solve other limits involving trig functions.  42, 45, o5, o6, o7
+<li> Know the "periodicity" of differentiation of trig functions--i.e. the fourth derivative of the sine function is again the sine function.  o3
+<li> Use the definition of the derivative plus the limits [2] and [3] to prove that the derivative of sin(x) is cos(x), and to prove that the derivative of cos(x) is -sin(x).  20
+</ol>
 ----
-== Section 3.1 (Drew) ==
+=== Section 3.4 ===
-Homework:
+Homework:<br>
-  Written:  2, 13, 17, 20, 25, 28, 29, 33, 55, 61, 77
+Written: 7, 24, 25, 31, 37, 47, 63, 65, 71, 84, 89<br>
-  Online:  Kill o6 last part, o14, o8
+Online: o1 - o 14
-Goals:
+'''Goals'''
-.  Compute derivatives using:
+<ol>
-    a.  The power rule.  Especially, be able to rewrite functions so the power rule can be applied.  13, 17, 20, 25, 28, 29, o1, o3, o7, o8, o9, o10, o11, o12
+<li> Fluency in chain rule: Given a composition of functions, use the chain rule and other rules to compute its derivative quickly.  7, 25, 37, 47, o1, o2, o3, o4, o5, o6, o7, o8, o9, o10, o11
-    b.  The derivative of e^x.  2, 17, 28, o12
+<li> Given values of two functions and their derivatives at certain points, use the formal statement of the chain rule to compute the derivative of compositions of these functions.  63, 65, 71, o12, o13
-    c.  Sums, differences, and scalar multiples of functions you can differentiate with these rules. (almost all problems)
+<li> Given a word problem involving the composition of functions, compute rates of change. Interpret the meaning of the derivative as a particular rate of change.  84, o14
-.  Use the definition of the derivative and limit laws to:
+<li> Use the chain rule and definition of even/odd functions to prove properties of derivatives of even/odd functions.  89
-    a. Prove simple rules, including the power rule for n=-2, -1, -1/2, 1/2, 1, 2, as well as sum and difference rules.  61
+<li> Compute the derivative of a^x.  24, 31
-    b. Compute certain limits.  77
+</ol>
-.  Find a tangent line to the graph of a function at a given point.  33, 55, o2, o4, o5
+----
+=== Section 3.5 ===
+Homework:<br>
+Written: 3, 11, 12, 15, 18, 21, 23, 34, 41, 43, 57, 67 <br>
+Online: o1 - o13
+'''Goals'''
+<ol>
+<li> For an implicitly defined equation, use implicit differentiation to find<br>
+  - dy/dx. 3, 11, 12, 15, 18, 21, o1, o2, o8, o10, o12<br>
+  - dx/dy. 23<br>
+  - d^2y/dx^2.  34, o7
+<li> Find the tangent line to an implicitly defined function. 41, 43, o3, o9, o11, o13
+<li> Use implicit differentiation to prove formulas for inverse functions, including inverse trig functions.  57, 67
+<li> Use formulas for derivatives of inverse trig functions, as well as other differentiation rules, to compute derivatives.  o4, o5, o6
+</ol>
 ----
-== Section 3.2 (Rebecca) ==
+=== Section 3.6  ===
-Homework
+Homework:<br>
+Written: 15, 17, 24, 27, 33, 39, 44, 48, 51, 54<br>
+Online:  o1 - o14
-  Written:  2,11,13,23,24,32,33,47,49,55,57
+'''Goals'''
-  Online: As listed.
+<ol>
+<li> Use formulas for the derivative of log_a(x) and ln(x), along with other differentiation rules, to compute derivatives.  15, 17, 24, 27, 33, 51, o1, o2, o3, o7, o8, o12, o14
+<li> Use logarithmic differentiation and/or properties of logs to simplify and then differentiate.  Recognize which functions require logarithmic differentiation, and which derivatives become more convenient using logarithmic differentiation.  39, 44, 48, o4, o5, o6, o9, o10, o13
+<li> Know the formula for the number e as a limit.  Use it to compute other limits involving e.  54
+</ol>
-Goals
+----
-. Be able to apply the product rule to find the derivative of functions. 11,24,33,47,49,55,57,  02,04,05,06,07,09
+=== Section 3.8 ===
-. Be able to apply the quotient rule to find the derivative of functions. 2,13,23,24,32,47,49,  01,03,08,010,011
-. Be able to prove the product and quotient rules and variations. 55,57*
+Homework:<br>
+Written:  14, 15<br>
+Online:  o1 - o7
+'''Goals'''
+<ol> Use exponential functions to model each of the following:
+<li> Population growth.  o1, o3, o4
+<li> Radioactive decay.  Especially, know how to find half-life, or given half-life, find an equation.  o5, o6
+<li> Cooling.  14, 15
+<li> Interest.  o2, o7<br>
+    - Derive the formula for compounding interest in n periods (see section 1.3, number 60)<br>
+    - Use expression of e as a limit to find formula for continuously compounded interest. (In text, p 239)
+</ol>
 ----
-== Section 3.3 (Skyler/James) ==
+=== Section 3.9 ===
-Homework
+Homework:<br>
+Written: 5, 22, 33, 35, 37, 42<br>
+Online: o1 - o6
-  Written:  9, 10, 18, 20, 35, 42, 45, 49
+'''Goals'''
-  Online: As listed.  Change ordinal number suffixes on #3 (e.g. 83th makes no sense)
+<ol>
+<li> Solve related rates problems. (all homework problems)<br>
-Goals
+      a) Draw picture<br>
+      b) Recognize variables from the problem, and rates of change as their derivatives.<br>
-. Know derivatives for the 6 basic trig functions.  Be able to use these to compute derivatives of more complicated functions.
+      c) Write equations relating variables (using geometry, trigonometry).<br>
-. Know limits [2] and [3] in the book.  Be able to use these to solve other limits involving trig functions
+      d) Differentiate, remembering to use the chain rule.<br>
-. Know the "periodicity" of differentiation of trig functions--i.e. the fourth derivative of the sine function is again the sine function
+      e) Plug in specific values to determine the requested answer.
-. Be able to use trig identities to find derivatives and limits
+</ol>
-. Use trig derivatives in various real world problems.
 ----
+=== Section 3.10 ===
-== Section 3.4 (Savannah) ==
+Homework:<br>
+Written: 1,2,3,5,23,28,43,44<br>
+Online:  o1 - o4<br>
+(Merge both written and online with 3.11)
-Homework
-    Written: 7, 24, 25, 31, 37, 47, 63, 65, 71, 84, 89
+'''Goals'''
-    Online: Kill O6, O7, O8; Reorder problems (see Dr. Purcell); Add #77 from the book to online (change "particle" to "point")
+<ol>
+<li> Compute the linearization of a function at a point.  1, 2, 3, 5, o1, o2<br>
-Goals
+      - Explain the relationship between the linearization and the tangent line. 5, o2<br>
+      - Explain how linearization is useful. 23, 28, o4
-. Fluency in chain rule: Given a composition of functions, use the chain rule and other rules to compute its derivative quickly.  7, 25, 37, 47, O1, O2, O3, O9, O10, O11, O12, O13, O14, O15, O16
+<li> Use the linearization at a point x=a to approximate the value of a function f(a+epsilon).   23, 28, o2, o3, o4
-. Given values of two functions and their derivatives at certain points, use the formal statement of the chain rule to compute the derivative of compositions of these functions.  63, 65, 71, O4, O5
+</ol>
-. Given a word problem involving the composition of functions, compute rates of change. Interpret the meaning of the derivative as a particular rate of change.  84
-. Use the chain rule and definition of even/odd functions to prove properties of derivatives of even/odd functions.  89
-. Compute the derivative of a^x.  24, 31
 ----
-== Section 3.5 (Rebecca) ==
+=== Section 3.11 ===
-Homework
+Homework:<br>
+Written: 3, 7, 9, 15, 23, 29a, 33<br>
+Online: o5 - o7 (with section 3.10)
-   Written: 3,11,12,15,18,21,23,34,41,57 (Add 43,67)
+'''Goals'''
-   Online: Kill 03,014; Replace 08 with 35 from the book and make it online
+<ol>
+<li> Know and be able to apply definitions of cosh and sinh to:<br>
+     - Evaluate hyperbolic expressions at a point  3<br>
+     - Prove cosh and sinh identities  7, 9, 15<br>
+     - Find limits   23<br>
+     - Prove the formulas for derivatives of hyperbolic functions. 24
+<li> Prove the formulas for the derivatives of cosh^-1, and sinh^-1. 29a.
+<li> Use the formulas for derivatives of sinh, cosh, sinh^-1, cosh^-1 to compute derivatives.  33, o5, o6, o7
+</ol>
-Goals
-) For an implicitly defined equation find dy/dx, dx/dy, and d^2y/dx^2 using implicit differentiation.
-) Find the tangent line to an implicitly defined function.
-) Know the derivatives of the inverse trig functions.
 ----
-== Section 3.6 (Sam) ==
+== Chapter 4 ==
-----
+=== Section 4.1 ===
-== Section 3.8 (Jessica) ==
+Homework:<br>
+Written:  3, 7, 9, 10, 11, 13, 35, 40, 57, 60, 74, 76, 77<br>
+Online:  o1 - o8
-Homework:
+'''Goals'''
+<ol>
+<li> Given a graph, identify locations of absolute and local max's and min's, and absolute and local max/min values.  Conversely, given information about absolute and local max/min, sketch an example of a graph.  3, 7, 9, 10, 11, 13
-  Written:  14, 15
+<li> Find all critical numbers of a given function.  35, 40, o7, o8
-  Online:  kill o5 (pH scale)
-Goals:
+<li> Find absolute max/min values, and the points at which they occur, for a given function on a given interval.  57, 60, o1, o2, o3, o4, o5, o6,
-  Use exponential functions to model each of the following:
+<li> Using the definition of local max/min, prove various statements about max/min's.  74, 76, 77
-. Population growth.  o1, o3, o4
+</ol>
-. Radioactive decay.  o6, o7
-    Find half-life, or given half-life, find equation.
-. Cooling.  14, 15
-. Interest.  o2, o8
-    - Derive the formula for compounding interest in n periods o2, o8 (see also section 1.3, number 60)
-    - Use expression of e as a limit to find formula for continuously compounded interest.
 ----
-== Section 3.9 (Mark) ==
+=== Section 4.2 ===
-Homework
+Homework:<br>
+Written:  7, 15, 17, 28, 29, 30, 35<br>
+Online:  o1 - o7
-    Written: 5, 22, 33, 35, 37, 42
+'''Goals'''
-    Online: Kill O1, O4, O7, O8, O11, O12, O13; remove geometry formulas from online questions.
+<ol>
+<li> Know the statement of Rolle's theorem.  In particular, given a function, show that it satisfies (or does not satisfy) all conditions of Rolle's theorem, then find the numbers that satisfy the conclusion of Rolle's theorem.  o3, o4, o5
-Goals
+<li> Know the statement of the Mean Value theorem.  Given a function, show that it satisfies (or does not satisfy) all conditions of the Mean Value theorem, and then find the numbers that satisfy the conclusion of the Mean Value Theorem.  7, 15, o1, o2, o6
-. Solve related rates problems. (all homework problems)
+<li> Use Rolle's theorem and the Mean Value theorem to show various facts:<br>
-      a) Draw picture
+ - Show that an equation has at least one/ exactly one root.  17<br>
-      b) Recognize variables from the problem, and rates of change as their derivatives.
+ - Given particular functions, prove there exist points where the derivative satisfies required properties.  28, 35<br>
-      c) Write equations relating variables (using geometry, trigonometry)
+ - Given restrictions on the derivative of a function, prove the function satisfies certain properties.  29, o7, proof of Theorem 5 page 284, proof of Corollary 7 page 284 <br>
-      d) Differentiate, remembering to use the chain rule.
-      e) Plug in specific values to determine the requested answer.
+<li> Use corollary 7 to prove certain functions differ by a constant.  30
+</ol>
 ----
-== Section 3.10 (Tyler) ==
+=== Section 4.3 ===
-Homework
+Homework:<br>
- Written 1,2,3,5,23,28,43,44
+Written: 1, 6, 7, 21, 23, 25, 28, 31, 72<br>
- Online Kill O4, O5, Renumber so that O3 is first and O1 is third.  Possibly add one more.  Change the hint in O1 to read "Try using linear approximation..."
+Online:  o1 - o4
+'''Goals'''
+<ol>
+<li> Know and apply the increasing/decreasing test to determine where a function f is increasing/decreasing<br>
+ - Given a graph of f, f', or f''.  1, 6, 31, o4<br>
+ - Given an algebraic expression for f. o1, o3
+<li> Find local maxima and minima using first and second derivative tests<br>
+ - Given a graph for f'. 6, 31, o4<br>
+ - Given an algebraic expression for f.  21<br>
+ - Given information about values of f' and f'' at a point.  23
+<li> Know the definition of concavity and how to determine concavity (the concavity test).  31, 72, o2, o3, o4
+<li> Know the definition of a point of inflection and how to find it.  7, 31, o4
+<li> Know how the above information affects the graph of a function.  Given intervals where first and second derivatives are positive and negative, sketch a graph.  25, 28
+</ol>
-Goals
-. Compute the linearization of a function at a point.  1,2,3,5, O2, O3
-      - Explain the relationship between the linearization and the tangent line. 5, O2
-      - Explain how linearization is useful. 23,28
-. Use the linearization at a point x=a to approximate the value of a function f(a+epsilon).   23,28, O1, O2
-Suggestion: merge 3.10 and 3.11 for written as well as online.
 ----
-== Section 3.11 (Savannah) ==
+=== Section 4.4 ===
-----
+Homework:<br>
+Written: 4, 7, 15, 31, 33, 39, 47, 49, 57, 70, 71, 81<br>
+Online: o1 - o10
-== Section 4.1 (Rebecca) ==
+'''Goals'''
+<ol>
+<li> Know when to use L'Hospital's rule to solve a limit.  (All problems, particularly 4, 71, others)
+<li>  Use L'Hospital's rule to find limits of functions of the following indeterminate forms:<br>
+- infinity/infinity or 0/0.   7, 15, 33, 70, 81, o1, o3, o6<br>
+- Indeterminate products.  39, 08<br>
+- Indeterminate differences.  47, 49, o4, o7<br>
+-  Indeterminate powers.  57, o9, o10
+</ol>
 ----
-== Section 4.2 (Spencer) ==
+=== Section 4.5 ===
-----
+Homework:<br>
+Written:  5, 12, 32, 47, 49<br>
+Online:  o1 - o2
-== Section 4.3 (Sam) ==
+'''Goals'''
+<ol>
+<li> Use all of the following to draw graphs of functions: (all problems)<br>
+ * Algebraic Properties (Domain, intercepts, even/odd/periodic)<br>
+ * Limit Properties (Asymptotes, singularities, discontinuities)<br>
+ * Derivative Properties (Increasing/decreasing, extrema, concavity/inflection)
+</ol>
-Goals:
+----
-.  Know and apply the increasing/decreasing test o1, o5
+=== Section 4.7 ===
-.  Find local maxima and minima (First and Second derivative tests, endpoints) 21,23
-.  Know the definition of concavity and how to determine concavity (The concavity test) o2, o5, 72
-.  Know what an inflection point is and how to find it o2
-.  Know how the above information affects the graph of a function
-        Draw a graph such that....    25, 28
-        Given a graph, where is concavity positive, etc.?   1, 6, 7, 31 and a new online problem similar to problem 8 on page 295
+Homework:<br>
+Written: 7, 14, 31, 35, 41, 47, 66<br>
+Online: o1 - o6
-Changes:
+'''Goals'''
+<ol>
+<li> Convert word problems into formulas, and use methods for finding extreme values to solve optimization problems. Interpret your answer in terms of the original problem.  Types of problems:
+  <ul>
+     <li> Given a formula relating two quantities.  7, 41, o2<br>
+     <li> 2-dimensional geometric objects, including rectangles, triangles, circles.  (Know areas, similar triangle facts)  31, 47, 66, o1, o3, o5<br>
+     <li> 3-dimensional geometric objects, including rectangular boxes, cylinders, spheres, cones.  (Know volume, surface area) 14, 35, o4, o6
+  </ul>
+</ol>
-  o3 and o4 are to be moved to section 4.5 and a problem is to be added online that is like problem 8.
 ----
-== Section 4.4 ==
+=== Section 4.8 ===
-Homework:  4, 7, 15, 31, 33, 39, 47, 49, 57, 70, 71, 81
+Homework:<br>
+Written: 1, 2, 3, 4, 29<br>
-Goals:
+Online:  o1 - o3
-.  Know when to use L'Hospital's rule to solve a limit.  (All problems, particularly 4, 71, others)
-.  Use L'Hospital's rule to find limits of functions of the following indeterminate forms:
-    a.  infinity/infinity or 0/0   7, 15, 33, 70, 81, o1, o3, o6
-    b.  Indeterminate products  39, 08
-    c.  Indeterminate differences  47, 49, o4, o7
-    d.  Indeterminate powers  57, o9, o10
+'''Goals'''
+<ol>
+<li> Use Newton's Method to approximate roots/solutions of equations. 1, 2, 3, 4, 29, o1, o2, o3
+<li> Derive the formula for Newton's Method from the tangent line equation.
+<li> Give an example of a function 'f' and a starting point 'x_1' that makes Newton's Method fail.  4, o3
+</ol>
 ----
-== Section 4.5 (Skyler) ==
+=== Section 4.9 ===
-Goals:
+Homework:<br>
+Written: 12, 15, 20, 27, 33, 49, 51, 53, 67, 69, 74<br>
+Online: o1 - o10
-	Use all of the following to draw graphs of functions:
-	* Algebraic Properties (Domain, intercepts, even/odd/periodic)
+'''Goals'''
+<ol>
-	* Limit Properties (Asymptotes, singularities, discontinuities)
+<li> Use the Mean value Theorem to prove Theorem 1.
+<li> Memorize the table of anti-differentiation formulas on page 341 and relate it to the table of derivatives on the inside back cover of the book.  <br>
-	* Derivative Properties (Increasing/decreasing, extrema, concavity/inflection)
+  <ul>
+  <li> Use these formulas and Theorem 1 to find *all* antiderivatives of various functions.  12, 15, 20, 27, o5, o6, o7
-Written homework - as listed
+  <li> Use these formulas and Theorem 1 to find a unique anti-derivative with given values at specified points. 33, 51, 53, 67, 69, 70, 74, o1, o2, o3, o4, o8, o9, o10
-Online homework - pulled from 4.3 (O3 and O4)
+  </ul>
+<li> Use anti-differentiation to solve physical and economic problems, especially problems of motion. 67, 69, 70, 74, o3, o4
+</ol>
 ----
+== Chapter 5 ==
-== Section 4.7 ==
+=== Appendix E ===
+Homework:<br>
+Written: 1, 3, 5, 10, 11, 15, 17, 20, 23, 41, 43<br>
+Online: o1 - o9
+'''Goals'''
+<ol>
+<li> Write expanded sums in sigma notation, 1, 3, 5, 10 <br>
+  and expand sums written in sigma notation. 11, 15, 17, 20). <br>
+  Numerically evaluate sums. 23  <br>
+  Apply appropriate rules to distribute constants or expand sums of sums. o3, o4, o6.
+<li> Explicitly evaluate a sum (in sigma notation) in terms of 'n', where the summand
+      is a polynomial in x of degree at most 3.  Degree 0: o5; degree 1: o1, o2;
+      degree 2: o3, o4; degree 3: o5 <br>
+<li> Evaluate telescoping sums.  41
+<li> Evaluate limits of sums. 43, 06
+<li> Change the index of summation. o7, o8, o9
+</ol>
 ----
-== Section 4.8 (Mark) ==
+=== Section 5.1/5.2a ===
-Goals
+Homework:<br>
+Written:  5.1: 1a, 12, 18, 21, 26; 5.2: 5ab, 17, 29, 30, 70<br>
+Online:  o1 - o5
-. Use Newton's Method to approximate roots/solutions of equations.
-. Derive the formula for Newton's Method from the tangent line equation.
-. Give an example of a function 'f' and a starting point 'x_1' that makes Newton's Method fail.
-Homework
+'''Goals'''
+<ol>
+<li> Use left and right sums to approximate area under a continuous function. 5.1: 1a, o1
+<li> Use the definitions of area under the curve to write the area as a limit.
+Use the definition of integral to write the integral as a limit. Conversely, given a limit that represents the area under a curve or an integral, find the region whose area is given, or write the integral. 5.1: 18, 21; 5.2: 17, 29, 30, 70; o4, o5.
+<li> Approximate integrals by left and right sums. 5.2: 5ab, o3.
+<li> Calculate a net change.  Interpret total change problems as area problems. 5.1: 12, o2
+</ol>
-    Written: 1, 2, 3, 4, 29.
-    Online: Kill O1, Add new online problem with graph.
 ----
-== Section 4.9 (Tyler)==
+=== Section 5.2 ===
+Homework:<br>
+Written: 34, 37, 43, 47, 49, 50, 55, 63<br>
+Online: o1 - o8
-Goals:
+'''Goals'''
-. Use the Mean value Theorem to prove Theorem 1.
+<ol>
-. Memorize the table of anti-differentiation formulas on page 341 and
+<li> Evaluate a given integral by interpreting it in terms of area. 34, 37, o1, o2, o3, o4
-                              relate it to the table of derivatives on the inside back cover of the book.  12, 15, 20, 27, 33, 49, 51, O1-O12
+<li> Use properties of the definite integral to<br>
-. Use the table and Theorem 1 to find *all* antiderivatives of various functions.  12, 15, 20, 27, 49, 51
+     - Rewrite integrals  47, 50, o5<br>
-. Use Theorem 1 and known differentiation formulas to find a unique anti-derivative with given values at specified points. 33, 53, 67,
+     - Evaluate integrals  43, 49, o6<br>
-, 70, 74,O2,O3, O4,O5,O10, O11, O13
+     - Estimate integrals  55, o7, o8
-. Use anti-differentiation to solve physical and economic problems, especially problems of motion. 67, 69, 70, 74, O4, O5
+<br> Use the definition of the definite integral to prove properties of the definite integral. 63
+</ol>
-Changes to problems:
-  Written:  Add story problems: 67, 69, 70, 74
-  Online: too long, Delete O1, O6, O12.
-                              Adjust numbers in 04 to give a clean answer.
-                              O10--change so that F(0) not equal to 0 (else they will get right answer for wrong reason).
-                              O8 and O9 problem that Arctan/Arcsin not accepted--just arctan/arcsin.
-                              O13 should not say "the anti-derivative, but rather "an anti-derivative".
 ----
-== Appendix E (Paul)==
+=== Section 5.3a  ===
-Homework:
-    Written: 1, 3, 5, 10, 11, 15, 17, 20, 23, 41, 43
+Homework:<br>
-    Online: o1, o2, o3, o4, o5, o6, o7, o8, o9, o10
+Written: 9, 15, 56, 57, 63, 64<br>
+Online: o1 - o8
-Goals
+'''Goals'''
+<ol>
+<li> Understand and explain the relationship between area and derivative described by the Fundamental Theorem.
+<li> Describe properties of functions defined by integrals, including their values at particular points, intervals where they are increasing/decreasing, maxima and minima, etc. 3, o7, 63, 64
+<li> Differentiate functions defined by integrals 9, 15, 56, 57, o1, o2, o3, o4, o5, o6, o8
+</ol>
-. Write expanded sums in sigma notation (1, 3, 5, 10)
-      and expand sums written in sigma notation (11, 15, 17, 20).
-      Numerically evaluate sums (23).  Apply appropriate rules to
-      distribute constants or expand sums of sums (o2, o4, o5, o8, o9, o10).
-. Explicitly evaluate $\sigma_{i=1}^n f(i)$ in terms of 'n', where 'f(x)'
-      is a polynomial in x of degree at most 3.  (Degree 0 o3, o7; degree 1
-      o1, o2, o10; degree 2 o4, o5.)
-      Numerically evaluate this sum when 'i' runs over a given range of integers (o6, o8, o9).
-. Evaluate telescoping sums (41) and limits of sums (43).
-. Change the index of summation.
-Kill o3, o6, o8, o9, o10, add written 30, 35, add 3 online problems on changing index of summation and one limit of a sum problem like 44.
 ----
-== Section 5.1 ==
+=== Section 5.3b ===
+Homework:<br>
+Written: 22, 31, 36, 41, 43, 59, 65, 66, 74<br>
+Online: o1 - o10
+'''Goals'''
+<ol>
+<li> Given a function and limits of integration verify that the hypotheses of the Fundamental Theorem hold. 43
+<li> Use the Fundamental Theorem to evaluate the definite integral of a function.  22, 31, 41, o1 - o10.  <br>
+Given the definite integral of a function, use the Fundamental Theorem to determine information about the function, or limits of integration.  59, 74
+<li> Recognize a limit of Riemann sums as a definite integral, and evaluate that definite integral using the Fundamental Theorem.  65, 66
+</ol>
 ----
-== Section 5.2 ==
+=== Section 5.4 ===
+Homework:<br>
+Written: 4, 9, 23, 32, 43, 49, 54, 59, 61, 65<br>
+Online: o1 - o10
+'''Goals'''
+<ol>
+<li> Evaluate definite and indefinite integrals for all standard functions
+      (polynomials 9, o1a, o3, o6a, o6c, rational functions 4, o1b, o1c, o4, o6b, o7, o8,
+      trigonometric functions and inverses 32, o5, o8, o9abc, o10, exponentials 23, 32 and
+      logarithms o8, absolute value 43, etc.)
+<li> Multiply, divide, substitute, or otherwise change the form of a function to make it easier to integrate.
+<li> Solve problems about net change by setting up and evaluating appropriate
+      integrals of rates of change (density 61, marginal cost 65,
+      displacement/distance o2, water flow o10, etc).
+</ol>
 ----
-== Section 5.3 (Tyler a, Ryan b)==
+=== Section 5.5a ===
+Homework:<br>
+Written:  5, 8, 9, 21, 25, 31, 38, 39<br>
+Online:  o1 - o9
-Goals:
+'''Goals'''
- A. Understand and explain the relationship between area and derivative described by the Fundamental Theorem.
+<ol>
- A. Evaluate and describe properties of functions defined by integrals 3, 5.3bO11,63,64
+<li> Use the substitution rule to evaluate indefinite integrals.  (all problems) <br>
- A. Differentiate functions defined by integrals 9,15, R44,R45,R47,R48,R68 , O1-O6
+<ul>
-  B. Given a function and limits of integration verify that the hypotheses
+<li> Become proficient in choosing a productive substitution. (all problems)  <br>
-               of the Fundamental Theorem hold
+<li> Use substitution to simplify a problem by substituting for more than one function or variable.  o5, o7
- B. Use the Fundamental Theorem to evaluate the definite integral of a function.
+</ul>
-  B. Apply the Fundamental Theorem to interpret the meaning of a
+</ol>
-                      definite integral and its derivative in physical, economic, and other applications.
-Problems:
-  A. written: 9,15,56,57,63,64
-  B. written: 22,31,36,41,43,59,65,66,74
-Changes to Online HW:
- A.  O5.  Make the hint part of the problem or make it not show until after they try once.
- A.  Move 5.3b O2
- A. Move 5.3bO11 to 5.3a, add to O11 an additional question about increasing and decreasing.
- A.   Kill O1
- B. O3 change arbitrary to right endpoint.
- B. Fix formatting
- B. Add one more limit problem (e.g., 24)
 ----
-== Section 5.4 (Paul)==
+=== Section 5.5b ===
-Homework:
-    Written: 4, 9, 23, 32, 43, 61, 65
+Homework:<br>
-    Online: o1, o2, o3, o4, o5, o6, o7, o8, o9, o10
+Written: 45, 46, 53, 73, 83<br>
+Online:  o1 - o10
-Goals
+'''Goals'''
+<ol>
-. Evaluate definite and indefinite integrals for all standard functions
+<li> Use the substitution rule to evaluate definite integrals.  53, o2, o3, o4, o5, o6, o7, o8, o9
-      (polynomials 9, o1a, o3, o6a, o6c, rational functions 4, o1b, o1c, o4, o6b, o7, o8,
+<li> Use substitution with other previously learned techniques to evaluate integrals, e.g. interpreting an integral as the area under a curve.  73
-      trigonometric functions and inverses 32, o5, o8, o9abc, o10, exponentials 23, 32 and
+<li> Use substitution to simplify a problem by substituting for more than one function or variable.  45, 46, o1, o4
-      logarithms o8, absolute value 43, etc.)
+<li> The substitution rule "undoes" one of the differentiation rules you learned in chapter 3.  Which rule?  o10
-. Solve problems about net change by setting up and evaluating appropriate
+</ol>
-      integrals of rates of change (density 61, marginal cost 65,
-      displacement/distance o2, etc.).
-----
-== Section 5.5 ==
 ----

Difference between revisions of "Math 112 Calculus Learning Goals"

Latest revision as of 22:21, 15 November 2009

Contents

Chapter 1

Section 1.1

Section 1.2

Trig to know, including problems to skim for practice.

Section 1.3

Section 1.5

Section 1.6

Chapter 2

Section 2.1

Section 2.2

Section 2.3a

Section 2.3b

Section 2.4

Section 2.5a

Section 2.5b

Section 2.6

Section 2.7

Section 2.8

Chapter 3

Section 3.1

Section 3.2

Section 3.3

Section 3.4

Section 3.5

Section 3.6

Section 3.8

Section 3.9

Section 3.10

Section 3.11

Chapter 4

Section 4.1

Section 4.2

Section 4.3

Section 4.4

Section 4.5

Section 4.7

Section 4.8

Section 4.9

Chapter 5

Appendix E

Section 5.1/5.2a

Section 5.2

Section 5.3a

Section 5.3b

Section 5.4

Section 5.5a

Section 5.5b

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