Mathematics and Coding on Physics 2 (past years)

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Old Documents

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