Math 447: Intro to Partial Differential Equations - Revision history

Ls5: /* Offered */

2019-11-14T16:55:20Z

‎Offered

Ls5: /* Offered */

2016-02-05T20:47:06Z

‎Offered

Ls5: moved Math 447 to Math 447: Intro to Partial Differential Equations

2013-04-03T22:11:48Z

moved Math 447 to Math 447: Intro to Partial Differential Equations

Cpg at 14:41, 19 July 2010

2010-07-19T14:41:57Z

Cpg: Trying to condense it.

2010-07-15T19:53:55Z

Trying to condense it.

Cpg: /* Minimal learning outcomes */

2010-07-15T19:32:36Z

‎Minimal learning outcomes

Cpg at 19:31, 15 July 2010

2010-07-15T19:31:32Z

Cpg: /* Minimal learning outcomes */

2010-02-18T16:59:33Z

‎Minimal learning outcomes

Cpg: /* Desired Learning Outcomes */

2010-02-18T16:57:43Z

‎Desired Learning Outcomes

Cpg: /* Minimal learning outcomes */

2010-02-18T15:18:47Z

‎Minimal learning outcomes

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 === Offered ===
-F (even years)
+W (even years)
 === Prerequisite ===

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 === Offered ===
-W, Su
+F (even years)
 === Prerequisite ===

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 #* Heat equation on bounded intervals, half-lines, lines, rectangles, disks, and balls
 </div>
 === Additional topics ===

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 #* Basic Sturm-Liouville theory
 #  Special eigensystems
-#* Fourier series
+#* Fourier
-#** Computation of the Fourier series of a ''p''-periodic function on an interval of length ''p''
+#** Series representations
-#** Computation of Fourier sine and cosine series of a symmetric ''p''-periodic function on an interval of length ''p''
+#*** Effect of symmetry and modifications and combinations of functions
-#** Fourier series of modifications and combinations of functions
+#*** Theorems on pointwise, uniform, and ''L''<sup>2</sup> convergence
-#** Theorems on pointwise, uniform, and ''L''<sup>2</sup> convergence
+#**** Bessel's Inequality and Parseval's Equation
-#** Bessel's Inequality and Parseval's Equation
+#** Integral representations
-#** Fourier integral representations of functions on lines and half-lines
+#* Bessel
-#* Bessel's equation and Bessel functions
+#* Legendre
-#* Legendre's differential equation and Legendre polynomials
 #  Representation of solutions to the canonical equations on simple domains
-#* Laplace's equation
+#* Laplace's equation on rectangles, rectangular strips, quarter-planes, half-planes, disks, and balls
-#** Eigenfunction expansion of solutions on rectangles
+#* Wave equation on bounded intervals, half-lines, lines, disks, and balls
-#** Integral representation of solutions on rectangular strips, quarter-planes, and half-planes
+#* Heat equation on bounded intervals, half-lines, lines, rectangles, disks, and balls
-#** Bessel function expansion of solutions on disks
-#** Legendre polynomial expansion on balls
 #* Wave equation
-#** Fourier expansion of solutions on bounded intervals
-#** D'Alembert's formula for solutions on lines and half-lines
-#** Bessel function expansion of solutions on disks
-#** Legendre polynomial expansion on balls
 #* Heat equation
-#** Steady-state solutions for IBVPs on bounded intervals
-#** Fourier expansion of solutions on bounded intervals
-#** Integral representation of solutions on lines and half-lines
-#** Eigenfunction expansion of solutions on rectangles
-#** Bessel function expansion of solutions on disks
-#** Legendre polynomial expansion of solutions on balls
 </div>

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 #* Derivation of the heat equation
 #* Derivation of the wave equation
 #  Basic principles, techniques, and theory
 #* Principle of superposition

← Older revision	Revision as of 22:11, 3 April 2013
(No difference)

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 #  Basic classification of PDEs
-#* As nonlinear, linear homogeneous, linear inhomogeneous
+#* Linearity
-#* By order
+#* Homogeneity
-#* Of second-order linear PDEs in 2 variables as elliptic, parabolic, or hyperbolic
+#* Order
 #  Basic Modeling
 #* Derivation of the heat equation

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 === Minimal learning outcomes ===
-Primarily, students should be able to calculate solutions to basic PDEs.  Students should gain a basic understanding of issues concerning solvability and convergence, but the current prerequisites don't guarantee that incoming students will have had any prior exposure to the theory of the convergence of sequences of functions, so expectations in that area are modest.
+Primarily, students should be able to use the solution techniques described below.  Students should gain a basic understanding of issues concerning solvability and convergence, but the current prerequisites don't guarantee that incoming students will have had any prior exposure to the theory of the convergence of sequences of functions, so expectations in that area are modest.
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 == Desired Learning Outcomes ==
 === Prerequisites ===
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 === Minimal learning outcomes ===
-The focus of the course is on bringing students to the point that they can solve the canonical linear second-order partial differential equations on simple domains.  Students should also gain some understanding of the theory about the reliability of these solution methods.  With the current prerequisites, however, students can't be counted on to have had any prior exposure to the theory of the convergence of sequences of functions, so theoretical understanding probably needs to be a secondary goal.
+Primarily, students should be able to calculate solutions to basic PDEs.  Students should gain a basic understanding of issues concerning solvability and convergence, but the current prerequisites don't guarantee that incoming students will have had any prior exposure to the theory of the convergence of sequences of functions, so expectations in that area are modest.
 <div style="-moz-column-count:2; column-count:2;">