For exceptional course registration (異常處理/加簽), you are advised to send an email to Sho by (at the latest) February 28th. (Still, the lecture room has a finite area.)
Outline
An intermediate-level mathematics course designed for physics learners. The course introduces linear algebra, Fourier analysis, basic special functions, and methods of numerical analysis. Rigorous mathematical foundations and detailed proofs are not the focus of this course. Instead, students are expected to be familiar with each topic and understand how to apply it to typical problems.
Prerequisites for this course include a basic understanding of calculus, matrix arithmetic, and ordinary differential equations. The course begins with linear algebra; you focus on the practical handling of matrices, including eigenvalue problems and matrix diagonalization. After the midterm exam, you learn fundamental ideas of function analysis, in particular Fourier analysis and basic special functions, as a natural continuation of the fall semester lecture.
The course also introduces fundamental concepts of numerical analysis. Students will gain necessary knowledge of numerical methods as well as practical skills using Python.
Students’ Goals
- I can perform basic matrix operations by hand and understand the roles of rank and determinants in linear algebra.
- I can solve simple eigenvalue problems and diagonalization problems by hand.
- I can carry out basic Fourier analysis of functions.
- I am familiar with basic special functions and understand where and why they appear.
- I understand the basic features and limitations of the IEEE-754 floating-point standard.
- I can apply numerical methods to typical problems in linear algebra and related topics.
Guidance document
- pm2_supplemental_2025.pdf for Academic Year 2025
- 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.
- You are assumed to have learned Chapters 1‒2 and 9‒10.
- This lecture covers Chapters 7‒8 and some parts of Chapters 5, 11, and 19‒21.
Schedule (2025‒2)
- 1 (Feb. 23, 26)
- Introduction: Logic.
- 2 (Mar. 2, 5)
- Matrices and Linear systems of Equations.
- 3 (Mar. 9, 12)
- Rank and Linear independence.
- 4 (Mar. 16, 19)
- Determinant and Inverse Inverse.
- 5 (Mar. 23, 26)
- Eigenvalue problem.
- 6 (Mar. 24, 2)
- Matrix with special names.
- 7 (Apr. 9)
- Matrix diagonalization.
- 8 (Apr. 13, 16)
- Midterm Exam (on Apr. 13) / Exam Review
- 9 (Apr. 20, 23)
- Modern programming. IEEE-754 Floating point numbers.
- 10 (Apr. 27, 30)
- Basic numerical analysis.
- 11 (May 4, 7)
- Fourier series expansion.
- 12 (May 11, 14)
- Fourier transformation.
- 13 (May 18, 21)
- Gamma function. Review of ODE.
- 14 (May 25, 28)
- Orthogonal polynomials.
- 15 (Jun. 1, 4)
- Bessel function.
- 16 (Jun. 8, 11)
- Term Exam (on Jun. 8) / Exam Review
Other Information
- Past exam problems are available at Sho’s Learning Resource page.
- See another page for previous years’ lectures.