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