This is an exercise course corresponding to the lecture course Applied Mathematics for Physicists and Scientists (IIZUB.M213).
Students will be able to deepen their understanding by solving problems related to the lecture course.
At the end of this course, students will be able to solve elementary problems of Fourier transform, special functions, and partial differential equations.
Fourier transform, gamma function, Legendre functions, Bessel functions, Hermite functions, Lagerre functions, partial differential equations, Green functions, Dirichlet problems, Laplace transform
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
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- | - | ✔ | - | - |
In every 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 | |
---|---|---|
Class 1 | Review of Fourier expansion and Fourier transform | Review the problems given in the exercise class. |
Class 2 | Inverse Fourier transform, Dirac's delta function | Review the problems given in the exercise class. |
Class 3 | Distribution, application to differential equations | Review the problems given in the exercise class. |
Class 4 | Gamma function | Review the problems given in the exercise class. |
Class 5 | Stirｌing formula, Beta function | Review the problems given in the exercise class. |
Class 6 | Legendre functions | Review the problems given in the exercise class. |
Class 7 | associated Legendre functions | Review the problems given in the exercise class. |
Class 8 | Spherical harmonics | Review the problems given in the exercise class. |
Class 9 | Bessel functions | Review the problems given in the exercise class. |
Class 10 | Hankel functions, Neumann functions | Review the problems given in the exercise class. |
Class 11 | modified Bessel functions, spherical Bessel functions | Review the problems given in the exercise class. |
Class 12 | Hermite functions, Laguerre functions | Review the problems given in the exercise class. |
Class 13 | partial differential equations, Dirichlet problems | Review the problems given in the exercise class. |
Class 14 | Green functions | Review the problems given in the exercise class. |
Class 15 | Laplace transform | Review the problems given in the exercise class. |
Not required
Not required
examination
Enrollment in Applied Mathematics for Physicists and Scientists II (ZUB.M213) is strongly recommended.