### 2020　Applied Mathematics for Physicists and Scientists II

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Physics
Instructor(s)
Sasamoto Tomohiro
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Tue3-4(H116)  Fri3-4(H116)
Group
-
Course number
ZUB.M213
Credits
2
2020
Offered quarter
2Q
Syllabus updated
2020/9/18
Lecture notes updated
-
Language used
Japanese
Access Index

### 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.

### Keywords

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

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