| 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 6.3-6.15 on the following .pdf |
|
| Monday January 25 |
Holomorphic
functions Functions of a complex variable, limits and continuity, holomorphicity. |
Chapter 2 | |
| Wednesday January
27 |
The Cauchy--Riemann 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: 2-8. Exercises 6.17-6.25 on the following .pdf Recommended (not for credit): Section 1.6: 9-14, 16-18. |
| 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 multiple-valued 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 21-March 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 Schwartz--Christoffel 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 |
z-transforms. | ||
| 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 |