2020 Applied Mathematics for Physicists and Scientists II

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Academic unit or major
Sasamoto Tomohiro 
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Tue3-4(H116)  Fri3-4(H116)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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Course description and aims

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.

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

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/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 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

Out-of-Class Study Time (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.


Not specified

Reference books, course materials, etc.

Not specified

Assessment criteria and methods

Based on small exams, reports ,etc

Related courses

  • ZUB.M201 : Applied Mathematics for Physicists and Scientists 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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