Lectures and exercises are coupled together in this course. Using what was learned in the lecture to actually solve problems with exercises reinforces the understanding gained from the lecture.
This course covers mathematics required in all physics courses in the Department of Earth and Planetary Sciences for subsequent terms, and are indispensable for understanding the mathematical basis for earth and planetary sciences. The aim of this course is for students to clearly understand basic concepts such as vector operations, differential equations, and the Fourier transform and their significance and to nurture the necessary mathematical ability.
By the end of this course, students will have acquired the mathematical basis required for understanding earth and planetary sciences and knowledge of the following:
1) Vector operations
2) Solution of ordinary and partial differential equations
3) The Fourier transform
4) The delta function and Green’s functions
vector, scalar, differential equation, Fourier transform, Laplace transform, Gauss divergence theorem
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Towards the end of class, students are given exercise problems related to what is taught on that day to solve.
Course schedule | Required learning | |
---|---|---|
Class 1 | Vector analysis | Understand vector analysis |
Class 2 | Vector analysis (gradient, divergence, rotation) | Understand vector analysis |
Class 3 | Gauss divergence theorem and Stokes theorem | Understand surface integral and volume integral |
Class 4 | Vector analysis for cylindrical coordinates and polar coordinates | Understand vector analysis for cylindrical and polar coordinates |
Class 5 | 1st order differential equation | Understand 1st order differential equation |
Class 6 | Constant-coefficient 2nd order differential equation | Understand constant-coefficient 2nd order differential equation |
Class 7 | simultaneous differential equations | Understand simultaneous differential equations |
Class 8 | variable coefficient linear differential equation | Understand variable coefficient linear differential equation |
Class 9 | complex analysis | Understand complex analysis |
Class 10 | Fourier series and Fourier transform | Fourier series and Fourier transform |
Class 11 | Delta function and Green's function | Understand Delta function and Green's function |
Class 12 | partial differential equation | Understand partial differential equation |
Class 13 | boundary value problem for ordinary differential equation | Understand Laplace transform |
Class 14 | boundary value problem for ordinary differential equation | Understand boundary value problem for ordinary differential equation |
Class 15 | comprehension check | Check the understanding of this course |
None required.
None required
Students’ course scores are based on final exams and exercise problems.
No prerequisites.