This page contains past lectures’ information,
For the ongoing lecture, see another page. For past exam problems and administrative documents, see Sho’s Learning Resource Page.
Textbook
E. Kreyszig, Advanced Engineering Mathematics, 10th ed. Taiwan custom version, Wiley (2018).
2023 Spring Semester
An intermediate-level mathematics course designed for physics learners. We will cover linear algebra, Fourier analysis, special functions, and methods of numerical analysis. Prerequisites for this course include a foundational understanding of calculus, vector and 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. Motivated students are expected to reach the concept of vector space. You then learn basic topics of function analysis, in particular Fourier analysis and special functions.
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.
- I am familiar with matrices and vectors. In particular, I can explain “vector space”, “basis”, “linear transformation”, “matrix rank”, and “eigenvectors”.
- I can perform Fourier analysis of functions and explain its physical interpretation.
- I know several special functions and their basic properties.
- Utilizing computers and online resources, I can numerically solve problems in linear algebra.
- I can use Python to find numerical solutions to basic differential equations.
150 min lecture for 18 weeks.
- 1 (Feb. 19, 22)
- Matrix and vector.
- 2 (Feb. 26, 29)
- Rank. Vector space. Determinant. / Setup of coding environment.
- 3 (Mar. 4, 7)
- Introduction to numerical analysis. / Linear-equation system.
- 4 (Mar. 11, 14)
- Vector space.
- 5 (Mar. 18, 21)
- Eigenvalue problem.
- 6 (Mar. 25, 28)
- Matrix diagonalization.
- 7 (Apr. 1)
- Summary of linear algebra.
- 8 (Apr. 8, 11)
- Midterm Exam / Exam review.
- 9 (Apr. 15, 18)
- Fourier series.
- 10 (Apr. 22, 25)
- Strum--Liouville problems.
- 11 (Apr. 29, 2)
- Fourier transformation.
- 12 (May 6, 9)
- Special functions.
- 13 (May 13, 16)
- Special functions. Frobenius Method.
- 14 (May 20, 23)
- Numerical analysis.
- 15 (May 27, 30)
- Numerical analysis.
- 16 (Jun. 3, 6)
- Term Exam / Exam review.
- 17 (Jun. 13)
- Flexible learning week (no class), compensating fo coding assignments.
- 18 (Jun. 17, 20)
- Topics requested by students.
2024 Spring Semester
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.
- 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.
150 min lecture for 18 weeks.
- 1 (Feb. 17, 20)
- Matrices and vectors.
- 2 (Feb. 24, 27)
- Linear systems of Equations.
- 3 (Mar. 3, 6)
- Rank.
- 4 (Mar. 10, 13)
- Determinant. Inverse.
- 5 (Mar. 17, 20)
- Eigenvalue problem.
- 6 (Mar. 24, 27)
- Matrices with special names.
- 7 (Mar. 31)
- Diagonalization and bases.
- 8 (Apr. 7, 10)
- Midterm Exam / Exam review
- 9 (Apr. 14, 17)
- Numeric linear algebra.
- 10 (Apr. 21, 24)
- IEEE-754 floating point numbers.
- 11 (Apr. 28, 1)
- Basic numerical analysis.
- 12 (May 5, 8)
- Review of ODEs.
- 13 (May 12, 15)
- Numerics for ODEs.
- 14 (May 19, 22)
- Fourier series expansion.
- 15 (May 26, 29)
- Fourier transformation.
- 16 (Jun. 2, 5)
- Term Exam / Exam review
- 17 (Jun. 9, 12)
- Review on complex numbers. Basic group theory.
- 18 (Jun. 16, 19)
- No class: Alternative learning period compensating for coding assignments
2025 Spring Semester
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.
- 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.
150 min lecture for 16 weeks.
- 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 / 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 / Exam Review