2024 Faculty Courses School of Science Undergraduate major in Physics
Mathematical Methods in Physics II（Lecture)
- Academic unit or major
- Undergraduate major in Physics
- Instructor(s)
- Katsushi Ito
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Tue / 3-4 Fri
- Class
- -
- Course Code
- PHY.M211
- Number of credits
- 200
- Course offered
- 2024
- Offered quarter
- 2Q
- Syllabus updated
- Mar 17, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course consists of lectures and exercises, and contains the basics of the Fourier transform, special functions, partial differential equations, and the Laplace transform.
The aim is for students to be able to use these methods without hesitation when solving physics problems in the future.
Course description and aims
At the end of this course, students will be able to apply Fourier transform, special functions, partial differential equations, and Laplace transform to problems in physics.
Keywords
Fourier transform, gamma function, Legendre functions, Hypergeometric functions, Confluent hypergeomeric functions, Orthogonal polynomials, Bessel functions, Hermite functions, Laguerre functions, partial differential equations, Laplace transform
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Lectures are given. In lecture class a (few) report problems may be assigned.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Review of Fourier expansion and Fourier transform | Understand the Fourier transform as a limit of the Fourier expansion. |
| Class 2 | Inverse Fourier transform, Dirac's delta function | Understand the definition of the delta function |
| Class 3 | Distribution, application to differential equations | Try solving some differential equations by using Fourier transform |
| Class 4 | Gamma function | Understand the definition of the Gamma function |
| Class 5 | Stirling formula, Beta function | Derive the Stirling formula |
| Class 6 | Hypergeometric functions | Understand the definition of hypergeometric functions |
| Class 7 | Legendre functions | Understand the definition of Legendre functions |
| Class 8 | Orthogonal polynomials | Understand basic properties of orthogonal polynomials. |
| Class 9 | Confluent hypergeometric functions | Understand the definition of confluent hypergeometric functions |
| Class 10 | Hermite functions, Laguerre functions | Derive formulas of Hermite and Laguerre polynomials from their generating functions |
| Class 11 | Bessel functions | Understand the definition of Bessel functions |
| Class 12 | modified Bessel functions, spherical Bessel functions | Understand the relation among modified Bessel functions, spherical Bessel functions, and Bessel functions. |
| Class 13 | Laplace transform | Explain differences between Laplace and Fourier transformations |
| Class 14 | Partial differential equation | Understand how to solve partial differential equations |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
Not required
Reference books, course materials, etc.
Not required
Evaluation methods and criteria
Based on reports and exam
Related courses
- PHY.M204 ： Mathematical Methods in Physics I
Prerequisites
Students are required to have completed Applied Mathematics for Physicists and Scientists I