Problem list for Math 403:01, spring 2002

Note Odd-numbered problems have bare answers or hints in the back of the book.

Section Section titleSuggested problems
1.1 Complex Numbers and the Complex Plane 1b,d,f,g 2b,c 4 5b,f 11 13a
1.1.1 A Formal View of the Complex Numbers No problems assigned.
1.2 Some Geometry 2 7 21 24 35 36
1.3 Subsets of the Plane 2 3 8 10 18a 19a,b
1.4 Functions and Limits 1 2 11 15 19 36 37
1.5 The Exponential, Logarithm, and Trigonometric Functions 2 4 8 9 11 17 19 23 24 25 27 28
1.6 Line Integrals and Green's Theorem 1 2 4 5 7 15
2.1 Analytic and Harmonic Functions; the Cauchy-Riemann Equations 1 6 14 16 17 20c,e
2.2 Power Series 2 3 5 14 18 19 22
2.3 Cauchy's Theorem and Cauchy's Formula 1 2 4 7 8 9 10 14 17 18a
2.3.1 The Cauchy-Goursat Theorem No problems assigned.
2.4 Consequences of Cauchy's Formula 1 2 3 5 7 9 10 11 13 17 18 20 21 24a
2.5 Isolated Singularities 3 4 6 7 8 9 13 14 15 21 22b,c
2.6 The Residue Theorem and its Application to the Evaluation of Definite Integrals 2 3 5 9 10 13 16 17 21 23a 26b
3.1 The Zeros of an Analytic Function 5 7 11 15 17a,c 20
3.2 Maximum Modulus and Mean Value 1 2 5 7 10 16
3.3 Linear Fractional Transformations 4a,bc,e 5a,c,e 7a,d 8b
3.4 Conformal Mapping 1 3a 7a,b 10
3.5 The Riemann Mapping Theorem and Schwarz-Christoffel Transformations 1 2 5 7 8 9
4.1 Harmonic Functions 1a,b,e 2 6 12 16

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