Math 532: Complex Analysis - Revision history

Ls5: /* Catalog Information */

2019-11-14T17:03:36Z

‎Catalog Information

2011-04-19T15:51:32Z

2011-04-19T15:41:15Z

‎Desired Learning Outcomes

2011-04-19T15:41:05Z

‎Desired Learning Outcomes

2011-04-19T15:40:54Z

‎Desired Learning Outcomes

2011-04-19T15:37:59Z

‎Desired Learning Outcomes

2011-04-19T15:26:14Z

‎Additional topics

2011-04-19T15:08:11Z

2010-07-28T16:24:37Z

‎Minimal learning outcomes

2010-05-25T17:32:34Z

‎Minimal learning outcomes

← Older revision		Revision as of 17:03, 14 November 2019
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	=== Credit Hours ===		=== Credit Hours ===
	3		3
		+
		+	=== Offered ===
		+	On demand (contact department)

	=== Prerequisite ===		=== Prerequisite ===

@@ Line 36: / Line 36: @@
 === Additional topics ===
 These are at the discretion of the instructor as time allows. Some possible additional topics include:
 '''Modular Functions and Theta Functions.''' The modular group, Eisenstein series, product formula for Jacobi theta function, transformation laws of theta functions, application to sums of squares.

@@ Line 35: / Line 35: @@
 === Additional topics ===
-These are at the discretion of the instructor as time allows. Some possible additional topics include: '''Modular Functions and Theta Functions.''' The modular group, Eisenstein series, product formula for Jacobi theta function, transformation laws of theta functions, application to sums of squares.
+These are at the discretion of the instructor as time allows. Some possible additional topics include:
 === Courses for which this course is prerequisite ===
 [[Category:Courses|532]]

@@ Line 24: / Line 24: @@
 #'''The gamma and zeta functions.''' Analytic continuation of gamma function, further properties of &Gamma;, functional equation and analytic continuation of zeta function.
 #'''Conformal mappings.''' Conformal equivalence, Schwarz lemma, Montel's theorem, Riemann mapping theorem.
 <div style="-moz-column-count:2; column-count:2;">
@@ Line 34: / Line 35: @@
 === Additional topics ===
-These are at the discretion of the instructor as time allows. Some possible additional topics include: '''Elliptic Functions and Theta Functions.''' Liouville theorems, Weierstrass elliptic functions, the modular group, Eisenstein series, product formula for Jacobi theta function, transformation laws of theta functions, application to sums of squares.
+These are at the discretion of the instructor as time allows. Some possible additional topics include: '''Modular Functions and Theta Functions.''' The modular group, Eisenstein series, product formula for Jacobi theta function, transformation laws of theta functions, application to sums of squares.
 === Courses for which this course is prerequisite ===
 [[Category:Courses|532]]

@@ Line 24: / Line 24: @@
 #'''The gamma and zeta functions.''' Analytic continuation of gamma function, further properties of &Gamma;, functional equation and analytic continuation of zeta function.
 #'''Conformal mappings.''' Conformal equivalence, Schwarz lemma, Montel's theorem, Riemann mapping theorem.
 <div style="-moz-column-count:2; column-count:2;">
@@ Line 35: / Line 34: @@
 === Additional topics ===
-These are at the discretion of the instructor as time allows. Some possible additional topics include: Weierstrass elliptic functions, the modular group, Eisenstein series, product formula for Jacobi theta function, transformation laws of theta functions, application to sums of squares.
+These are at the discretion of the instructor as time allows. Some possible additional topics include: '''Elliptic Functions and Theta Functions.''' Liouville theorems, Weierstrass elliptic functions, the modular group, Eisenstein series, product formula for Jacobi theta function, transformation laws of theta functions, application to sums of squares.
 === Courses for which this course is prerequisite ===
 [[Category:Courses|532]]

← Older revision	Revision as of 15:51, 19 April 2011
(No difference)

← Older revision		Revision as of 16:24, 28 July 2010
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	</div>		</div>
		+	=== Textbooks ===
		+
		+	Possible textbooks for this course include (but are not limited to):
		+
		+	*

	=== Additional topics ===		=== Additional topics ===

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 === Minimal learning outcomes ===
 Students should be familiar with the following concepts. They should know the technical terms, and be able to implement the methods taught in the course to work associated problems, including proving simple results.
-#'''Essential results from a first course.''' Review of power series, integration along curves, Gourset theorem, Cauchy's theorem in a disc, Taylor series, Morera's theorem, singularities, residue calculus, Laurent series, argument principle, harmonic functions, maximum modulus principle.
+#'''Essential results from a first course.''' Review of power series, integration along curves, Goursat theorem, Cauchy's theorem in a disc, Taylor series, Morera's theorem, singularities, residue calculus, Laurent series, argument principle, harmonic functions, maximum modulus principle.
 #'''Entire functions.''' Jensen's formula, functions of finite order, Weierstrass infinite products, Hadamard factorization theorem.
 #'''The gamma and zeta functions.''' Analytic continuation of gamma function, further properties of &Gamma;, functional equation and analytic continuation of zeta function.