Date  Topics covered  Reading  Homework Assignments 
Monday January 12 
Review of
complex numbers 
Chapter 1 

Wednesday January 14 
Complex exponential, powers and roots. 

Friday January 16 
The Riemann sphere and stereographic
projection. 
HW1: Due Friday Feburary 6 Chapter 1 Exercises: Section 1.1 #2,15,26 Section 1.2 #1,4,8,20,21 Section 1.3 #2,5,22 Section 1.4 #3,9,23 Section 1.5 #4,17 Section 1.6 #28 Recommended (not for credit): Section 1.6 #914, 1618 

Monday January 19 
NO CLASS 
NO CLASS  
Wednesday
January 21 
Holomorphic functions Functions of a complex variable, limits and continuity, holomorphicity. 
Chapter 2  
Friday January
23 
The CauchyRiemann
equations. 
HW 2: Due Friday February 6 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 January 26 
Elementary functions Polynomials and rational functions, the exponential function. 
Chapter 3  
Wednesday January 28 
Trigonometric
and hyperbolic functions, the logarithmic function, washers,
wedges and walls. 

Friday January 30 
Complex powers and inverse trigonometric functions, applications.  HW 3: Due Friday February 6 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 3.4 #1,2,3 Section 3.5 #1,5,6,11 

Monday
February 2 
Analytic functions Sequences and series, Taylor series, Power series. 
Chapter 5 

Wednesday
February 4 
Convergence, Laurent series,
zeros and singularties. 
Read the following pdf on convergence.  
Friday
February 6 
The point at infinity,
analytic continuation. 
HW 5: Due Friday February 20 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 9 
Homework review 

Wednesday February 11 
Review  
Friday
February 13 
MIDTERM I 
MIDTERM
I 

Monday
February 16 
Complex integration. Contours, contour integrals, independence of path. 
Chapter 4 
HW 4: Due Friday February 27 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 
Wednesday
February 18 
Cauchy's integral theorem, Cauchy's integral formula and its consequences.  
Friday
February 20 
Bounds for holomorphic functions, applications.  
Monday February 23 
Reside theory Residue theorem, trigonometric integrals. 
Chapter 6 

Wednesday February 25 
Improper integrals.  
Friday February 27 
Improper integrals involving trigonometric functions.  HW 6: Due Friday March 6 Chapter 6 Exercises: Section 6.1 #1,2,3,7 Section 6.2 #1,2,3 Section 6.3 #1,2,3,8 

Monday
March 2 
Indented contours. 

Wednesday
March 4 
Integrals involving multiplevalued functions.  

Friday
March 6 
The argument theorem and Rouche's theorem.  HW 7: Due Friday April 3 Chapter 6 Exercises: 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 9 
Conformal mapping  Chapter 7  
Wednesday March 11 
Harmonic functions. Invariance of Laplace's equation.  
Friday March 13 
Geometric considerations.  HW 8: Due Friday April 10 Chapter 2 Exercises: Section 2.5 #1,5,9,10,20,21 Chapter 7 Exercises: Section 7.1 #1,2,3 Section 7.2 #1,2,3,4,5,10,11,14 

Monday
March 16 
Homework review 

Wednesday
March 18 
Review  
Friday
March 20 
MIDTERM II 

Week of
March 23March 27 
SPRING BREAK  SPRING BREAK  
Monday March 30 
Mobius transformations.  

Wednesday April 1 
The SchwartzChristoffel transformation.  
Friday April 3 
Applications.  
HW 8: Due Friday April 17 Chapter 7 Exercises: Section 7.3 #1,2,3 Section 7.4 #5,10,11,12,21,22 Section 7.5 #1,3,4 
Monday
April 6 
Transforms in complex
analysis Fourier series. 
Chapter 8 

Wednesday
April 8 
Fourier transforms.  
Friday
April 10 
Fourier transforms continued, and Laplace transforms.  HW 9: Due Friday April 24 Chapter 8 Exercises (not to be turned in) 

Monday April 13 
Laplace transforms continued. 

Wednesday April 15 
ztransforms.  
Friday April 17  Cauchy integrals and the Hilbert transform.  HW 10: Due Friday April 24 Chapter 8 Exercises (not to be turned in) 

Monday
April 20 
Further topics 

Wednesday
April 22 
Further topics 

Friday
April 24 
Further topics 
HW 11: Due Friday May 1 Study for final exam 

Monday April 27 
Further topics 

Wednesday April 29 
Homework review 

Friday May 1 
Review 

Thursday May 7 
FINAL
EXAM 1:30 
4:00 PM ECCR
118 (Lecture Room) 
FINAL EXAM  FINAL EXAM 