Professor: Richard Borcherds
Office hours: WF 1:00-2:30
927 Evans Hall
Our class meets in 3 Evans Hall (changed from Cory), 9:30-11:00, Tuesdays and Thursdays. This is the course home page (address www.math.berkeley.edu/~reb/121).
Prerequisites: 53 and 54. Functions of a complex variable, Fourier series, finite-dimensional linear systems. Infinite-dimensional linear systems, orthogonal expansions, special functions, partial differential equations arising in mathematical physics. Intended for students in the physical sciences who are not planning to take more advanced mathematics courses.
Math 121B will cover chapters 11, 12, 13, and 16 of the text. The topics will be special functions, series solutions of differential equations, partial differential equations, and probability.
Mathematical methods in the physical sciences by M. L. Boas, second edition, published by Wiley.
The grading will probably be somthing like homework 40%, midterms 15% each, and final 30% of the grade. The final grade is not based on a curve or on previously fixed marks for certain grades. Instead the average grade for the course will be based on my judgement of how well the class is doing, and will be high if everyone is working hard at the homework and doing well on the exams.
Almost all the questions in the midterms or finals will be randomly selected questions from the book similar to homework questions, possibly with the constants in the questions changed. So if you understand how to do all the homework questions you will be able to do all the questions on the exams.
I only change grades for exams or quizzes if there is a clear error on the part of the grader, such as adding up marks incorrectly or forgetting to grade a question. Grades for incomplete answers will never be increased, because this is unfair to students who do not ask for their grades to be increased. I will not increase grades just because someone needs a higher grade to graduate or get into some program.
The final homework grade will be computed from the grades for the 10 or so best homeworks, so it does not matter much if you forget one or two.
You may use a pocket calculator in the exams. You may also bring one (ordinary sized!) sheet of paper with writing on both sides to the exams. Apart from this one sheet, the exams are "closed book".
The first midterm is on Feb 19.
The second midterm is on April 1.
The final is on May 18, 8:00-11:00am (Exam group 9) It will be mostly on the material covered after the second midterm, though there will be some problems on earlier material.
Homework is due by the end of the Tuesday lecture 1 week after it is assigned. Late homework will not be accepted. 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. 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.
| Lecture | Date | Reading | Exercises (Due in class the next Tuesday) |
| 01-02 | Jan 20-22 | 11.1-11.7, 11.11 | Chapter 11: 3.4, 3.8, 3.13, 4.5, 4.7, 5.1, 6.1, 6.2, 7.3, 7.7, 7.9, 11.2, 11.5, 11.8, 11.9. Gamma function table and calculator |
| 03-04 | Jan 27-29 | 11.9, 11.10, 11.12 | Chapter 11: 9.1, 9.3, 9.4, 10.3, 10.5, 10.13, 10.14, 12.1, 12.2, 12.7, 12.9, 12.16, 12.18, 12.21 Elliptic integral table , Error function table |
| 05-06 | Feb 3-5 | 12.1-12.5 | Chapter 12: 1.1, 1.11, 1.16, 2.1, 2.2, 2.3, 3.5, 4.3, 4.4, 5.1, 5.3, 5.5, 5.6, 5.7, 5.11. |
| 07-08 | Feb 10-12 | 12.6-12.10 | Chapter 12: 6.4, 6.5, 6.6, 7.3, 7.4, 7.5, 8.2, 9.1(first 3 terms), 9.6(first two terms), 9.11, 9.14, 10.1, 10.2, 10.5 |
| 09 | Feb 17 | ||
| 10 | Feb 19 | Midterm | |
| 11-12 | Feb 24-26 | 12.11-12.15 | Chapter 12: 11.2, 11.6, 12.5, 12.6, 12.8, 12.9, 13.1, 13.2, 13.5, 14.1, 14.3, 15.1, 15.2, 15.3, 15.5, 15.7, Bessel function table |
| 13-14 | Mar 2-4 | 12.16-12.21 | Chapter 12: 16.3, 17.2, 17.5, 17.7, 17.10, 17.12, 19.1, 19.2, 19.3, 20.1, 21.13, 21.18, 21.15(terms in 1, x, x2) |
| 15-16 | Mar 9-11 | 12.22, 13.1 | Chapter 12: 22.1, 22.4, 22.5, 22.7, 22.8, 22.12, 22.13, 22.15, 22.18, 22.27 Chapter 13: 1.1, 1.2, 1.3 |
| 17 -18 | Mar 16-18 | 13.2-13.3 | Chapter 13: 2.1, 2.3, 2.7, 3.2, 3.3, 3.7, 3.9, 3.10, |
| -- | Mar 22- 26 | ------------- | (Spring Break ) | 19 | Mar 30 |
| 20 | Apr 1 | --- | Midterm |
| 21-22 | Apr 6-8 | 13.4, 13.5 | Chapter 13: 4.1, 4.2, 4.6, 5.1, 5.2, 5.4, 5.11 |
| 23-24 | Apr 13-15 | 13.6-8 | Chapter 13: 6.1, 6.2, 6.3, 7.2, 7.15, 7.16, 7.17, 8.1, 8.2, 8.3, 8.4 |
| 25-26 | Apr 20-22 | 16.1-2 | Chapter 16: 1.1, 1.2, 1.3, 1.4, 1.5, 1.8, 1.10, 2.12, 2.13, 2.14, 2.15, 2.17, |
| 27-28 | Apr 27-29 | 16.3-4 | Chapter 16: 3.4, 3.5, 3.10, 3.12, 3.14, 3.15, 3.16, 3.17, 3.19, 3.21 4.1, 4.4, 4.5, 4.7, 4.8, 4.10, 4.11, 4.15, 4.17, 4.21 |
| 29-30 | May 4-6 | 16.5-16.9 | Chapter 16: 5.1, 5.3, 5.7, 7.1, 7.7, 8.1, 8.5, 8.7, 9.3, 9.5, 9.8. |
| 31 | May 11 | ||
| -- | May 18, 8:00-11:00am | 3 Evans | Final Exam: |