In preparation; any information here may be changed later.
Outline
An intermediate-level mathematics course designed for physics learners. We will cover linear algebra, Fourier analysis, and methods of numerical analysis. Prerequisites for this course include a foundational understanding of calculus, matrix arithmetic, and ordinary differential equations.
After reviewing the basics of matrices, you first learn linear algebra with an emphasis on practical handling of matrices and eigenvalue problems. You then learn fundamentals of function analysis, particularly Fourier analysis.
Additionally, the course introduces fundamental concepts in numerical analysis and basic numerical methods for mathematical problems such as ordinary differential equations. Students will gain theoretical knowledge in numerical analysis as well as practical coding skills in Python, using the contemporary Python ecosystem.
This course does not cover the mathematical foundations of each topic. Instead, students are expected to be familiar with the topics and develop an appreciation of their usefulness.
Students’ Goals
- I am familiar with matrix calculation. In particular, I know why rank and determination are important and can calculate them by hand.
- I can diagonalize simple matrices.
- I can perform Fourier analysis of functions.
- I understand the basic property of IEEE-754 floating point numbers.
- Utilizing Python and online resources, I can numerically solve problems in linear algebra, basic differential equations, or other topics learned in the previous semesters.
Guidance document
- pm2_supplemental_2025.pdf for Academic Year 2025 (in preparation)
- Hints for Writing and Submitting Assignments
Textbook
E. Kreyszig, Advanced Engineering Mathematics, 10th ed. Taiwan custom version, Wiley (2018).
- Sho will often refer to it during the lecture, assuming you all have the textbook ready.
- Attendants are assumed to have learned Chapters 1‒2 and 9‒10. We discuss Chapters 7‒8, 11, and 19‒21.
Schedule (2025‒2)
- 1 (Feb. 23, 26)
- 2 (Mar. 2, 5)
- 3 (Mar. 9, 12)
- 4 (Mar. 16, 19)
- 5 (Mar. 23, 26)
- 6 (Mar. 30, 2)
- 7 (Apr. 9)
- 8 (Apr. 13, 16)
- 9 (Apr. 20, 23)
- 10 (Apr. 27, 30)
- 11 (May 4, 7)
- 12 (May 11, 14)
- 13 (May 18, 21)
- 14 (May 25, 28)
- 15 (Jun. 1, 4)
- 16 (Jun. 8, 11)
Past Exam Problems
Other Information
- See another page for previous years’ lectures.