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Math 121B: Mathematics for Physical Sciences
UC Berkeley, Spring 2020
Zoom Meeting: https://berkeley.zoom.us/j/486973340
MWF 9-10AM
Zoom Office hours: MWF: 10-11am, and Monday Friday afternoon 4-5pm.
My Personal Meeting ID is: 881-910-2324.
Please also join the chat channel, named “Math 121B”. So that if I am not in my 'office' during office hour, you can send me a message, and I will be back.
Instructor
Peng Zhou (pzhou.math@berkeley.edu)
Office: 931 Evans
Office Hour: MWF: 10-11am, M:12-1pm. W:2-4pm.
Syllabus
We continue to use the textbook by Boas, Mathematical Methods in the Physical Sciences 3rd edition.
We will cover chapters 10, 11, 12, 13, 15. We split them into two parts
Part I: Ch 10, 13.1-4. Chapter 10 is about tensor notation and curvilinear coordinates, which will be used in Ch 13 to do separation of variable for Laplace operator $\Delta$, and reduce PDE to ODEs.
Part II: Chapter 12 is about solving these ODEs, and the solutions are Bessel function and Legendre function. Finally, after these hard works, we can tackle Chapter 13 for various PDEs in physics.
Part III: Ch 15, We will learn basic probability concepts. If time permits, we will do some topics on probability, such as central limit theorems, stochastic processes, or markov chain.
Exams
We will have two midterms and one final. midterms are for part I and II, and final is accumulative.
Homeworks
Homeworks will be assigned weekly, but not collected or graded. You are welcome to submit for comments.
Grading Total grade = 30% + 30% for the two midterms + 40% final.
Accomodation
If you are a DSP student and need accomodation for exams, please let me know at the beginning of the semester.
Piazza Please sign up at https://piazza.com/berkeley/spring2020/math121b
References
These are excerpts of the book Finite Dimensional Vector Spaces, written by Paul R. Halmos.
The whole book can be found in our library with online access, or directly here .
“A good stock of examples, as large as possible, is indispensable for a thorough understanding of any concept, and when I want to learn something new, I make it my first job to build one.” – Paul Halmos
Problems
Lectures
Week 1
2020-01-22, Wednesday: What is a vector? We will review 3.10 and 3.14. A vector space without choosing a basis is quite OK.
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Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
03-02: More on generating function. Orthogonality of Legendre polynomial. Boas 10.5 - 10.7
03-04: Associated Legendre function. Boas 0
03-06: Started Bessel functions.
Week 8:
Week 9:
03-16:
note Beta function 1 11.7
03-18:
note Generating Function of Bessel function. Begin Stationary phase expansion.
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Week 11
Week 12
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04-10:
ipad note (corrected a mistake about orthogonality of $P_l^m(x)$.
Midterm 2: take home midterm, from Friday evening to Sunday midnight. Exam will be release through piazza. The test will cover Boas chapter 11 (Beta function and Gamma function), 12, 13 (except Integral transform section). It will not cover things outside of Boas, example: steepest descend method.
Week 13
Week 14
Week 15