2017 Mathematical Methods in Physics II B

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Academic unit or major
Undergraduate major in Physics
Imamura Yosuke  Yokoyama Takehito  Adachi Satoshi 
Course component(s)
Lecture / Exercise
Day/Period(Room No.)
Tue3-6(3-4:H116 5-6:H115)  Fri3-6(3-4:H116 5-6:H115)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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Course description and aims

This course consists of lectures and exercise, 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.

Student learning outcomes

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.


Fourier transform, gamma function, Legendre functions, Bessel functions, Hermite functions, Laguerre functions, partial differential equations, Green functions, Dirichlet problems, Laplace transform

Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills
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Class flow

In lecture class students are sometimes given exercise problems for assessment of understanding.
After every class students should review the topic in the class.
In every exercise class students will be given some problems and solve them.
Solutions will be explained in the latter half of the class.

Course schedule/Required learning

  Course schedule Required learning
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 Midterm exam to assess the students’ level of understanding on what has been taught so far and explanation of solutions Review the course contents so far
Class 9 Bessel functions Derive formulas of Bessel functions from their generating function
Class 10 Hankel functions, Neumann functions Understand the relation between Hankel and Neumann functions and Bessel functions
Class 11 modified Bessel functions, spherical Bessel functions Understand the relation among modified Bessel functions, spherical Bessel functions, and Bessel functions.
Class 12 Derive formulas of Hermite and Laguerre functions from their generating functions. Derive formulas of Hermite and Laguerre functions from their generating functions.
Class 13 partial differential equations, Dirichlet problems Understand the uniqueness of the solution of a Dirichlet problem.
Class 14 Green functions Derive the Green function for the Laplace operator.
Class 15 Laplace transform Understand the relation between Laplace transform and Fourier transform


Not required

Reference books, course materials, etc.

Not required

Assessment criteria and methods

Students' course scores will be based on midterm and final exams in the lecture class
and term paper in the exercise class.

Related courses

  • PHY.M204 : Mathematical Methods in Physics I

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students are required to have completed Applied Mathematics for Physicists and Scientists I

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