### MATH 295: Complex Analysis

MATH 295 - Syllabus

Office hours: M 9.00-10.00, F 10.00-12.00 (in Innovation 450)

1  M 8.26 Basic operations on complex numbers. 1.1,1.2
W 8.28 More basics 1.3,1.4
F 8.30 Sets, domains, regions,... 1.5 HW 1(due: 9/6)
2  M 9.2 Labor Day
W 9.4 open/closed sets, complex functions 1.5,2.1 HW 2(due: 9/11)
F 9.6 polynomials, periodic functions, parametric curves 2.1,2.2 HW1 DUE HW1-Sols
3  M 9.9 linear mappings 2.3
W 9.11 power functions 2.4 HW2 DUE, HW 3(due: 9/18),HW2-Sols
F 9.13 Reciprocal functions 2.5
4  M 9.16 limits of complex functions 3.1
W 9.18 limits of complex functions 3.1 HW 4(due: 9/25) HW3-Sols
F 9.20 more limits (epsilon-delta proof), continuity 3.1
5  M 9.23 multiple valued functions and branches (log n) 3.1
W 9.25 more branch cuts/points, start on derivatives 3.1, 3.2 HW4 DUEHW 5(due: 10/2), HW4-Sols
F 9.27 Cauchy-Riemann 3.3
6  M 9.30 Harmonic functions, Laplace's equation 3.4
W 10.2 Review for M1
F 10.4 Midterm 1 Practice, Pr-Sols M1, M1-Sols
7  M 10.7 Complex exponential and logarithm revisited 4.1 HW 6(due: 10/18)HW5-Sols
W 10.9 More logarithms and the complex power function 4.2
F 10.11 (hyperbolic) sines and cosines 4.3 HW 7(due: 10/18)
M 10.14 Fall Recess
W 10.16 plotting sin(z) and intro to integrals 5.1
F 10.18 complex integrals 5.1 HW6-Sols HW7-Sols
8  M 10.21 Quiz 1Quiz 1 Sols, Integral bounds 5.2+notes HW 8(due: 10/28)
W 10.23 Cauchy-Goursat 5.3
F 10.25 Path independence 5.4
9  M 10.28 Review of deformation of contours 5.3
W 10.30 Cauchy's integral formulas 5.5 HW 9(due: 11/6)HW8-Sols
F 11.1 Maximum modulus 5.5+notes
11  M 11.4 Finishing off T5 5.5
W 11.6 Sequences and Series 6.1 HW9-Sols
F 11.8 Taylor Series 6.2 HW 10(due: 11/13)
12  M 11.11 Laurent series 6.3
W 11.13 isolated singularities and zeros 6.4 HW10-Sols
F 11.15 Midterm 2 M2 M2-Sols HW11(due: 11/20)
13  M 11.18 Zeros and poles 6.4
W 11.20 Residues 6.5
F 11.22 Residues, more examples 6.6+notes HW11-Sols
14  M 11.25 BREAK
W 11.27 BREAK
F 11.29 BREAK HW12
15  M 12.2 Laplace/Fourier transforms 6.7+notes
W 12.4 Jordan's lemma and more weird integrals Quiz 2
F 12.6 Application to gradient fields