2020 Students Enrolled in or before 2015 School of Science Physics
Applied Mathematics for Physicists and Scientists II
- Academic unit or major
- Physics
- Instructor(s)
- Tomohiro Sasamoto
- Class Format
- Lecture (Zoom)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Tue (H116) / 3-4 Fri (H116)
- Class
- -
- Course Code
- ZUB.M213
- Number of credits
- 200
- Course offered
- 2020
- Offered quarter
- 2Q
- Syllabus updated
- Jul 10, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course explains 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, Bessel functions, Hermite functions, Laguerre functions, partial differential equations, Green functions, Dirichlet problems, Laplace transform
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
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 | Legendre functions |
Derive formulas of Legendre functions from their generating function. |
| Class 7 | associated Legendre functions, Spherical harmonics |
Understand the relation between associated Legendre functions and spherical harmonics. |
| Class 8 | Bessel functions |
Derive formulas of Bessel functions from their generating function |
| Class 9 | Hankel functions, Neumann functions |
Understand the relation between Hankel and Neumann functions and Bessel functions |
| Class 10 | modified Bessel functions, spherical Bessel functions |
Understand the relation among modified Bessel functions, spherical Bessel functions, and Bessel functions. |
| Class 11 | Hermite functions, Laguerre functions |
Derive formulas of Hermite and Laguerre functions from their generating functions. |
| Class 12 | partial differential equations, Dirichlet problems |
Understand the uniqueness of the solution of a Dirichlet problem. |
| Class 13 | Green functions |
Derive the Green function for the Laplace operator. |
| Class 14 | Laplace transform |
Understand the relation between Laplace transform and Fourier transform |
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 specified
Reference books, course materials, etc.
Not specified
Evaluation methods and criteria
Based on small exams, reports ,etc
Related courses
- ZUB.M201 ： Applied Mathematics for Physicists and Scientists I
Prerequisites
Students are required to have completed Applied Mathematics for Physicists and Scientists I