This page is still under construction
Professor: Richard Borcherds
Office hours: 927 Evans Hall, 9:30-11:00 Tu Th. email: reb followed by @ math dot berkeley dot edu
The class meets in 123 Wheeler, 3:30-5:00 Tu Th. The Course Control Number is 54661 This is the course home page (address /~reb/185).
Analytic functions of a complex variable. Cauchy's integral theorem, power series, Laurent series, singularities of analytic functions, the residue theorem with application to definite integrals. Some additional topics such as conformal mapping.
This section will probably cover chapters 1-7 of the textbook.
Complex Variables and Applications, by James Ward Brown, Ruel V. Churchill. ISBN-13: 978-0071263283
The publisher's price is $70 (not $170 as the ASUC store seems to claim), the ASUC store sometimes sells second hand copies, and you should be able to find second hand copies for about $50 from Abebooks or Amazon.
Homework will account for about 30% of the grade.
Midterm 1 will account for about 20% of the grade.
Midterm 2 will account for about 20% of the grade.
The final will account for about 30% of the grade.
Almost all the questions in the midterms or finals will be similar to homework questions or problems discussed in class.
Each question on the midterms and final will be worth 3 points. The grading scheme is: 3 points for a completely correct and clear answer in simplified form, 2 points for an essentially correct answer with some minor errors, 1 point for a reasonable start on the question, 0 points for no significant progress. It is your responsibility to make your answers clear: if you get the question right but the grader does not notice, then this is your fault for not making your answer clear enough, and you will lose points for it. Students will never get extra partial credit by asking for it, as this is unfair to students who do not ask. Marks for exams will only be changed if there is a clear error on the part of the grader, such as adding up marks incorrectly or forgetting to mark a question.
If you miss the first midterm the mark for the second midterm will be doubled. If you miss the second then the mark for the final will be increased to make up for this. If you miss both midterms or the final then you are in trouble. There will be no makeup midterms or finals.
The final homework grade will be computed from the grades for the 10 best homeworks, so it does not matter much if you forget one or two. About half the marks for homework will be based on the number of questions that you made a serious attempt on, and about half will be based on more detailed marking of a few questions.
You may not use a pocket calculator in the exams. You may bring one sheet of paper with writing on both sides to the exams. Apart from this one sheet, the exams are "closed book".
Homework is due by the end of the Tuesday lecture the week after it is assigned. Late homework will not be accepted. Collaboration on homework is fine, but if you hand in similar homework to your collaborator you should clearly state so and say who you are working with, in order to avoid unfortunate misunderstandings.
For each lecture, you should read the section of the textbook, and do the homework exercises listed below.
| Lecture | Date | Reading | Exercises (Due in class the next Tuesday) |
| 1 | 8-27 | 1.1-1.5 | 1.2.1, 1.2.4, 1.2.6, 1.2.11, 1.3.1, 1.4.1, 1.4.5, 1.5.1, 1.5.2, 1.5.15 |
| 2 | 9-1 | 1.6-1.10 | 1.8:1, 2, 5, 9, 10; 1.10:1, 2, 3, 7, 8 |
| 3 | 9-3 | 11-14 | 11:1, 2, 3. 12:1, 2, 4. 14:2, 3, 5, 7 |
| 4 | 9-8 | 14-18 | 18:1, 3, 5, 10, 11 |
| 5 | 9-10 | 19-22 | 20:1, 2, 3, 6, 7, 8 |
| 6 | 9-15 | 23-26 | 23:4, 7, 10. 25:1,4, 6. 26:1, 4, 5, 6 |
| 7 | 9-17 | 29-34 | 29:1, 8, 10, 11. 31: 1, 2, 11. 33: 1, 3, 9. 34:2, 15 |
| 8 | 9-22 | 37-41 | 38: 2, 3, 5. 39:1, 5, 6 |
| 9 | 9-24 | 43-48 | 42: 1, 8 43: 1, 2, 4, 7. 45:1, 2, 5 |
| 10 | 9-29 | First midterm solutions | |
| 14 | 10-13 | 55-59 | 56.4, 6, 9. 59:1, 3, 9, 10, 11, 12, 13 | 11 | 10-1 | 47-51 | 49:1, 2, 3, 4, 7, 9 |
| 12 | 10-6 | 27,50-52 | 52:1, 2, 3, 8 |
| 13 | 10-8 | 28, 53-54 | 28:2, 5. 54: 1,3,5, 7 9 |
| 14 | 10-13 | 55-59 | 56.4, 6, 9. 59:1, 3, 9, 10, 11, 12, 13 |
| 15 | 10-15 | 60-62 | 62:1,5, 7, 8, 10, 11 |
| 16 | 10-20 | 63-67 | 66:1, 4, 11, 67:1, 3, 4, 5, 6, 7, 8 |
| 17 | 10-22 | 68-71 | 71:1, 2, 4, 5, 6 |
| 18 | 10-27 | 72-74 | 72:1, 2, 5. 74:1, 2, 3, 5, 6, 7 |
| 19 | 10-29 | 75-77 | 76:1, 2, 3, 4, 5, 6 |
| 21 | 11-5 | 78-79 | 79: 1, 2, 3, 4, 5, 6, 7, 8, 9 |
| 22 | 11-10 | 80-81 | 81: 1, 2, 3, 4, 5, 6, 7, 8, 12 |
| 23 | 11-12 | 82-84 | 84: 4, 8 |
| 24 | 11-17 | 82-84, 85 | 84: 1, 2, 3, 6, 7. 85: 1, 4, 7 |
| 25 | 11-19 | 86-87 | 87: 1, 2, 5, 6, 7, 9 |
| 27 | 12-1 | 90-95 | 90:4, 6 92:2, 4, 5 94:1, 4, 5, 7, 10. 95: 3 |