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
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
In every exercise class students will be given some problems and solve them.
Some explanations of their solutions will also be given.
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、Laplace transform | Review the problems given in the exercise class. |
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
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Students' course scores are based on reports and presentations.
Enrollment in Applied Mathematics for Physicists and Scientists II (ZUB.M213) is strongly recommended.