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2025 (Current Year) 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 (W9-324(W933)) / 3-4 Fri (W9-324(W933))
Class
-
Course Code
PHY.M211
Number of credits
200
Course offered
2025
Offered quarter
2Q
Syllabus updated
Apr 2, 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) quiz and 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