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.
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, Hypergeometric functions, Confluent hypergeomeric functions, Orthogonal polynomials, Bessel functions, Hermite functions, Laguerre functions, partial differential equations, Laplace transform
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Lectures are given. In lecture class a (few) report problems may be assigned.
Basically in live format. A few times of lectures may be delivered by on-demand format as a trial (with interactive nature kept).
In every exercise class students will be given some problems and solve them.
Some explanations of their solutions will also be given. (This may change for online exercise,)
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 | 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 |
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
Based on reports, exam, etc
Students are required to have completed Applied Mathematics for Physicists and Scientists I