Homepage for  640:403 Spring 2004
Final exam: Allison Road Classroom Building 204
Thursday, May 6, 8-11PM

Sample problems for the final exam



Sample problems for second midterm

First midterm and answers
 

General Course Information


  Approximate Syllabus


 
Lecture Date Topics covered Sections fromText and Section(Assigned problem numbers parts)
1 01-20 Complex Numbers and the Complex Plane.
A Formal View of the Complex Numbers.
 1.1 (1b,d,f,g 2b,c 4 5b,f 11 13a),  1.1.1
2 01-22
 Some Geometry.
 1.2 ( 2, 7, 21, 24 ,35, 36)
3 01-27
 Subsets of the Plane. 1.3  (2, 3, 8, 10, 18a 19ab)
4 01-29
 Functions and Limits. 1.4 (1, 2, 11, 15, 19, 36, 37 )
5 02-03 The Exponential, Logarithm, and Trigonometric Functions
1.5 ( 2, 4, 8, 9, 11, 17, 19, 23, 24, 25, 27, 28 )
6 02-05
 The Exponential, Logarithm, and Trigonometric Functions (cont)
7 02-10 Line Integrals and Green's Theorem.
 1.6 (1, 2, 4, 5, 7, 15)
8
 2-12 1.6 (cont).
9 02-17 Analytic and Harmonic Functions; the Cauchy-Riemann Equations.
2.1 (1, 6, 14, 16, 17, 20ce)
10 02-19 Power Series.                                  2.2  (2, 3, 5, 14, 18, 19, 22)
11 02-24 Power Series (cont).
 2.2
12 02-26 Cauchy's Theorem and Cauchy's Formula
 The Cauchy-Goursat Theorem.
 2.3 (1, 2, 4, 7, 8, 9, 10, 14, 17, 18a), 2.3.1
13 03-02
 First Midterm.
 Through 2.2
14 03-04
 Cont. of 2.3; Consequences of Cauchy's Formula. 2.4 (1, 2, 3, 5, 7, 9, 10, 11, 13, 17, 18, 20, 21, 24a) 
15 03-09 Consequences of Cauchy's Formula  (cont).
 2.4 
16 03-11 Isolated Singularities.
 2.5  (3, 4, 6, 7, 8, 9, 13, 14, 15, 21, 22bc)
17 03-23 The Residue Theorem and its Application to the Evaluation of Definite Integrals.
 2.6 (2, 3, 5, 9, 10, 13, 16, 17, 21, 23a, 26b) 
18 03-25 Cont. of 2.6
2.6
19 03-30
 The Zeros of an Analytic Function.
 3.1 (5, 7, 11, 15, 17ac, 20)
20 04-01 The Zeros of an Analytic Function (cont).
 3.1
21 04-06 Maximum Modulus and Mean Value.
 3.2 (1, 2, 5, 7, 10, 16)
22 04-08 Linear Fractional Transformations.  3.3 (4abce, 5ace, 7ad, 8b)
23 04-13 Second midterm.
 Through 3.2
24 04-15 Conformal Mapping
3.4 (1, 3a, 7ab, 10)
25 04-20 The Riemann Mapping Theorem and Schwarz-Christoffel Transformations
3.5 (1, 2, 5, 7, 8, 9)
26 04-22 3.5 (cont)
 3.5
27 04-27 Harmonic Functions.
 4.1 (1abe, 2, 6, 12, 16)
28 04-29 Integral Representations of Harmonic Functions.
 4.3