(8/16) You can find out your grade for the class on TeleBears and your final exam score on bSpace.
(8/14) Final exam solutions are posted below.
(8/12) I am posting Notes for the special topic lecture tomorrow. They are not required reading, but you might wish to read them to understand more than I will have time to discuss in the lecture, and as further review of topics such as contour integrals, the residue theorem, and analytic continuation.
(8/11) The Final Exam is Thursday, August 14, covering all material on which homework has been assigned. See Exams, below, for details and practice exams.
(7/14) Reminder: the Midterm Exam is this Thursday, July 17, covering the material on homework assignments 1 through 4—for details, see Exams, below.
(7/10) You can check your homework and exam scores by logging into bSpace with your CalNet ID. The bSpace page for this class is MATH 185 LEC 001 Su14.
(7/3) Both class hours are in 9 Evans from now on.
(6/24) On Problem Set 1, there is a typo in the book on problem 11.6. It should say to factor z4+4, not z2+4.
(6/23) Welcome to Math 185! Check this page for announcements, homework assignments and solutions, etc.
You might be able to get by with the 8th edition, but please be aware that the exercises and the numbering of sections differ between the 8th and 9th editions, and some topics have been moved to different chapters.
Week 1: B&C Chapter 1, 2
The complex number system. Geometric picture of complex arithmetic. Exponential notation. N-th roots of a complex number.
Regions and domains in the complex plane.
Functions of a complex variable. Mappings on the complex plane.
Week 2: B&C Chapter 2 (continued)
Limits and continuity for functions of a complex variable. Limits at infinity.
Derivatives of functions of a complex variable. Cauchy-Riemann equations. Conditions for differentiability. Analytic functions.
Laplace equation and harmonic functions.
Week 3: B&C Chapter 3, 4
Exponentials, logs, complex powers, trig and hyperbolic trig functions and their inverses.
Contour integrals. Antiderivatives and the Cauchy-Goursat theorem.
Week 4: B&C Chapter 4 (continued), 5
Cauchy's integral formula.
Derivatives of analytic functions.
Liouville's theorem. Fundamental theorem of algebra. Maximum modulus principle.
Series and convergence for complex numbers. Power series, Taylor's theorem.
Week 5: B&C Chapter 5 (continued), 6
Analytic continuation, reflection principle (Chapter 2)
Laurent series and Laurent's theorem.
Absolute and uniform convergence. Circle of convergence. Uniqueness of series representations.
Singularities, poles, residues. Cauchy's residue theorem. Residues at infinity. Types of singularities.
Week 6: B&C Chapter 7
Calculation of integrals using the residue theorem.
Winding number, argument principle and Rouché's theorem.
Week 7: B&C 8, 9
Mappings defined by elementary functions. Linear fractional transformations.
Conformal mapping. Harmonic conjugates, transformation of harmonic functions and boundary conditions by a conformal map.
Week 8: B&C Chapter 9 (continued), 10
Applications of conformal mapping to Dirichlet and Neumann problems.
Special topic: the Riemann zeta function
Midterm Exam: Thursday, July 17 in both class hours. Covers the material on homework assignments 1 through 4, that is, Chapter 1 through Chapter 4 §53 in the text, omitting §28-29. Exam Questions and Solutions
Final Exam: Thursday, August 14 in both class hours. Covers all material on the reading and homework assignments, with more emphasis on material not already covered on the midterm. Wednesday's special lecture on the Riemann zeta function will not be covered on the exam, but can serve as a review, since I will use methods we have learned in the course. Exam Questions and Solutions
Here are links to some final exams from earlier years for practice. Note that they may have covered slightly different material from our class. Spring 2014 (Kozai), Spring 2013 (Liu), Summer 2012 (Lott)
Accommodations: Students needing special accommodations for exams must provide documentation from the Disabled Students' Program (DSP). Please let me know at the beginning of the course so that approriate arrangements can be made.
Homework will be due every Monday, except Problem Set 1, which will be due on Wednesday the first week. I will typically select 2 or 3 problems from each set to be graded.
You may discuss homework problems with others, but you must write your solutions independently, without copying from notes taken in group work. Taking solutions from the web or from previous years classes is not allowed.
| Lectures | Reading | Homework | Due |
|---|---|---|---|
| 6/23-24 | Chapter 1 §1-11 | Problem Set 1, Solutions* | Wed 6/25 |
| 6/25-26 | Chapter 1 §12 and 2 §13-14 | Problem Set 2, Solutions | Mon 6/30 |
| 6/30-7/3 | Chapter 2 §15-27 | Problem Set 3, Solutions | Mon 7/7 |
| 7/7-11 | Chapter 3 (all) and 4 §41-53 | Problem Set 4, Solutions | Mon 7/14 |
| 7/14-16 | Chapter 4 §54-59 and 5 §60-65 | Problem Set 5, Solutions** | Mon 7/21 |
| 7/17 | Midterm Exam | ||
| 7/21-24 | Chapter 5 §66-73, 2 §28-29 and 6 (all) | Problem Set 6, Solutions | Mon 7/28 |
| 7/28-31 | Chapter 7, omitting §95 | Problem Set 7***, Solutions | Mon 8/4 |
| 8/4-7 | Chapter 8, §96-108, and 9 (all) | Problem Set 8, Solutions | Mon 8/11 |
| 8/11-12 | Chapter 10 §118-126 | Problem Set 9, Solutions | Wed 8/13 |
| 8/13 | Optional: Notes on the Γ and ζ functions | ||
| 8/14 | Final Exam | ||
* Answer to problem (i) should be -2-4√3.
** Solution to Additional Problem 1 had several
mistakes. Corrected version
*** Exercises 90.x should be 91.x, and 93.5 should be 92.5.
No make-up exams or homework extensions will be given.
If you miss an exam without a documented valid reason, you will receive a score of 0 on the midterm, or a grade of F for the class if you miss the final.
If you miss the midterm because of a documented illness or emergency, your grade will be based 70% on final exam, 30% on homework.
If you miss the final because of a documented illness or emergency, please contact me about the possibility of receiving an Incomplete. Note that Incomplete grades can only be given to UC Berkeley students, and only if you have a passing grade on the work not missed.