Date  Topics covered  Reading  Homework Assignments 
Monday January 11 
Introduction 

Wednesday January 13 
Linear algebra Introduction to linear algebra. 
Read the following .pdf
on linear algebra 

Friday January 15 
Linear algebra continued. 
HW1: Due Friday January 15 Exercises: 1.48, 1.49, 1.55, 1.57, 1.59, on the following .pdf 

Monday January 18 
NO CLASS MLK 
NO CLASS MLK  
Wednesday
January 20 
Complex numbers Introduction to complex numbers. 
Chapter 1  
Friday
January 22 
Complex
exponential, powers and roots. The Riemann sphere and
stereographic projection. 
HW 2: Due Friday
January 22 Chapter 1 Exercises: Section 1.1: 2, 15, 26. Section 1.2: 1, 4, 8, 20, 21. Exercises 6.36.15 on the following .pdf 

Monday January 25 
Holomorphic
functions Functions of a complex variable, limits and continuity, holomorphicity. 
Chapter 2  
Wednesday January
27 
The CauchyRiemann equations.  
Friday January 29 
Elementary
functions
Polynomials and rational functions, the exponential
function. 
Chapter 3 
HW 3: Due Friday January 29 Chapter 1 Exercises: Section 1.3: 2, 5, 22. Section 1.4: 3, 9, 23. Section 1.5: 4, 17. Section 1.6: 28. Exercises 6.176.25 on the following .pdf Recommended (not for credit): Section 1.6: 914, 1618. 
Monday
February 1 
Trigonometric and hyperbolic functions, the logarithmic function, washers, wedges and walls.  
Wednesday
February 3 
Complex powers and inverse trigonometric functions, applications.  
Friday
February 5 
Analytic functions Sequences and series, Taylor series, Power series. 
Chapter 5 Read the following .pdf on uniform convergence. 
HW 4: Due Friday
February 5 Chapter 2 Exercises: Section 2.1: 1(a), (b), 5, 12, 14, 15 Section 2.2: 1, 2, 3, 5, 9, 18, 20, 22 Section 2.3: 2, 4, 6, 7(b), 14, 16 Section 2.4: 1, 2, 4, 10, 15 
Monday February 8 
Homework review 

Wednesday
February 10 
Review  
Friday February 12 
MIDTERM I 
MIDTERM I 

Monday February 15 
Convergence, Laurent series, zeros and singularities.  
Wednesday February 17 
The point at infinity, analytic continuation.  
Friday February 19 
Complex
integration. Contours, contour integrals, independence of path. 
Chapter 4  HW 5: Due Friday
February 19 Chapter 3 Exercises: Section 3.1:# 2, 3(a), 4, 7, 11, 14 Section 3.2:# 3, 7, 14, 18 Section 3.3:# 8, 9, 11 Section 3.5:# 1, 5, 6, 11 
Monday February
22 
Integration continued. 

Wednesday
February 24 
Cauchy's integral theorem, Cauchy's integral formula and its consequences.  
Friday February
26 
Bounds for holomorphic functions, applications.  HW 6: Due Friday February 26 Chapter 5 Exercises: Section 5.1: #1, 5, 6, 13, 16 Section 5.2: #1, 2, 5, 10, 13 Section 5.3: #1, 2, 3, 10, 12, 13 Section 5.5: #1, 3, 9 Section 5.6: #1, 2, 5, 6, 9 

Monday February 29 
Reside theory Residue theorem, trigonometric integrals. 
Chapter 6 

Wednesday March 2 
Improper integrals.  

Friday March 4 
Improper integrals involving trigonometric functions.  HW 7: Due Friday March 4 Chapter 4 Exercises: Section 4.1 #2, 3, 11 Section 4.2 #2, 3, 8, 12, 15 Section 4.3 #1, 2, 3, 4, 5, 10, 11, 12 Do the exercises on this .pdf. Recommended (not for credit): Section 4.4 #1, 3, 9, 11, 15 Section 4.5 #1, 2, 3, 6, 9, 10, 11 Section 4.6 #3, 4, 5, 6, 12, 14, 15 Section 4.7 #1, 2, 3, 4, 5, 6, 7, 8, 9 

Monday March
7 
Indented contours.  

Wednesday
March 9 
Integrals involving multiplevalued functions.  
Friday March
11 
The argument theorem and Rouche's theorem.  HW 8: Due Friday March 11 Chapter 6 Exercises: Section 6.1 #1, 2, 3, 7 Section 6.2 #1, 2, 3 Section 6.3 #1, 2, 3, 8 Section 6.4 #1, 2, 3 Section 6.5 #3, 4, 5 Section 6.7 #1, 2, 4, 5, 6 Recommended (not for credit): Section 6.3 #14, 15, 18 Section 6.7 #13, 14, 18 

Monday March 14 
Homework
review 

Wednesday March 16 
Review  
Friday
March 18 
MIDTERM II 

Week
of March 21March 25 
SPRING BREAK  SPRING BREAK  
Monday March
28 
Conformal mapping 
Chapter 7 

Wednesday March
30 
Harmonic functions. Invariance of Laplace's equation.  
Friday April 1  Geometric considerations 
HW 9: Due Friday April 8 Chapter 2 Exercises: Section 2.5 #1, 5, 9, 21 Chapter 3 Exercises: Section 3.4:# 1, 2, 3 Chapter 7 Exercises: Section 7.1 #1, 2, 3 Section 7.2 #2, 4, 5, 10, 14 Recommended (not for credit): Chapter 2 Exercises: Section 2.5 #10, 20 Chapter 7 Exercises: Section 7.2 #1, 3, 11 

Monday April 4 
Mobius transformations.  
Wednesday April 6 
The SchwartzChristoffel transformation.  
Friday April 8 
Applications.  HW 10: Due Friday April
15 Chapter 7 Exercises: Section 7.3 #1, 2, 3 Section 7.4 #5, 10, 11 Section 7.5 #1, 3, 4 Recommended (not for credit): Chapter 7 Exercises: Section 7.3 #1, 2, 3 Section 7.4 #12, 21, 22 

Monday April
11 
Transforms in complex analysis Fourier series. 
Chapter 8 

Wednesday
April 13 
Fourier transforms.  
Friday April 15  Fourier transforms continued, and Laplace transforms.  HW 11: Due Friday April 29 Chapter 8 Exercises: Section 8.1 #1, 7 Section 8.2 # 1(b), 3(a), 6(a), 7. 

Monday April 18 
Laplace transforms continued.  
Wednesday April 20 
ztransforms.  
Friday April 22 
Cauchy integrals and the Hilbert transform.  
Monday April 25 
Further topics 

Wednesday April
27 
Homework review 

Friday April 29 
Review 

Thursday May 5 
FINAL
EXAM 7:30 PM 
10:00 PM ECCR
118 (Lecture Room) 
FINAL EXAM  FINAL EXAM 