Instructor:
Peng Zhou, pzhou.math@gmail.com
Office Hours at 931 Evans Hall
Grading: Homeworks: 20% + Quizzes 10% + Midterms 30% + Final 40%
Textbook: Boas “Mathematical Methods in the Physical Sciences” 3rd. ed
Homeworks are due Tuesday in class.
Quizzes will be announced in the previous class. It is not taken regularly every week.
Midterm 1: Oct 8th
Midterm 2: Nov 7th
Final: December 18th, 8-11am
Week 1:
Lec 1 (9/3): Convergence of Sequences and Series. Test of convergences.
Lec 2 (9/5): Exercises for Lec 1. Power series and series expansion of functions.
Homework 1 (due on 9/10 in class) (...and small correction: problem 3, sum starts from n=2, not n=1)
Week 2:
Lec 3(9/10): Finishing Ch 2. More about Taylor expansion. Start Ch2
Lec 4(9/12): Quiz 1. Section 2.5, 2.6, 2.7
Homework 2: (Solution)
S1.13: #20,#22,#27,#33
S1.15, #6, #7, #19 #23.
S2.5: #5, #55, #62
S2.6 #8, #9(note, this is not absolute convergence. compare with example 2 above), #12, #13
S2.7 #3, #7, #12, #13, #16
S2.17 #13(hint: compare the real part and imaginary part from both sides), #16
Week 3:
Lecture 5(9/17): Review the quiz. Complex powers and roots. Sine, Cosine and exponentials.
Read Ch 2.11-13, do
Lecture 6(9/19): Quiz 2 on Ch 2. Start Ch 14. Cauchy-Riemann condition.
Homework 3
Ch 2: sec 9: #4, #6, #16, #18
sec 10: #15,#26
sec 11: #6, #13, #17
sec 12: #2, #3, #26, #28
sec 14: #1,2,3
Ch 14:
sec 1: #1, #3, #6, #7, #9, #13, #14
sec 2: #22, #23
Week 4:
Lecture 7(9/24): Review quiz 2. Finish 14.2
Lecture 8(9/26): singularity of analytic function; multi-valued function; examples of contour integral.
HW4: [Solution (thanks to Angelica)]
14.2 #34, #35, #36
6.8 #1,#2, #3
14.3 #1,2,4,5,7,8,12,15
Week 5:
HW5 (due on Oct 15)
14.3: #21,# 23,
14.4: #3, 5, 7, 9, 11
14.6: #5, 6, 9, 14, 16, 18, 24, 30, 31
[HW5 Solution] (correction: I wrote solution for 10(d) instead of 11(d). For 11(d), one get order 3 pole).
Midterm 1. Oct 8 (Tuesday in class)
[Practice problems] and solution
typos in problem #5: it should be changed to 1/(z+1) + 1/(z+2).
Week 6
Week 7:
HW 6:
(A) section 14.7 #3, #12, #14, #22
(B) In addition, if your midterm grade is <= 50, I would suggest you to work out corrections of the midterm.
Week 8:
Lecture note this week on Ch8. We covered up to 8.8. Skipped 8.4
HW7:
8.3 #1, #2, #11
8.5 #3, #11
8.6 #1, #2, #3
8.8 #1, #2, #8
Exposition: (there is no correct answer)
[Week 9]
Solution to HW6 posted
HW 8: Due next Thursday.
[Week 10]
Solution to HW7 posted.
Office hour this week: Monday 11:30 - 1:30pm. Tuesday 2-3pm.
11.5 Tuesday: Review and Examples.
11.7 Thursday: Midterm 2. and its solution , score distribution
No homework this week.
HW8 Solution posted
[Week 11]
HW9(Due Nov 21, Thursday):
7.5 #2 7.8 #11(a),(b) 7.11 #10 7.12 #9 7.13 #21
Fourier Transform lecture notes
[Week 12]
HW10, Due Thursday(12/5)
9.1 #2
9.2 #4, #5
9.3 #2, #6
9.5 #8, #11
[Week 13]
Office Hours this week:
(12/3) Tuesday: 2-4pm
(12/5) Thursday: 2-3pm
Final in previous years and Sample problems
2015 Sample Final, and solution
Previous exams: https://math.berkeley.edu/courses/archives/exams/math-121a. These exams may overlap, but not entirely coincide with our course materials, so you can use at your own discretion.
About Final:
Series and Sequence(10), Contour integral (20), Differential equation (e.g. chapter 8) (20) Green function(10) Fourier Transform(20), Variational Methods(20)
Formula that will be provided in case it is needed in the problem: Taylor expansion table (as in midterm 1), Laplace transformation table (as in midterm 2), the Gaussian Integral of exp(-x^2/2), Convolution formulae for Fourier and Laplace transformation.