This course covers the mathematical basis necessary for understanding the physical phenomena in Earth and planetary sciences. Especially, the mathematical skills learned in this course is fundamentally required in all geophysics courses in the Department of Earth and Planetary Sciences. The specific aim of this course is for students to clearly understand the basic concepts of the fundamental mathematics including vector operations, differential equations, and the Fourier transform, and to nurture the mathematical skill necessary for studying Earth and planetary science. Following the systematic explanation in the lecture, students learn mathematical knowledge and skills by solving problems proactively throughout exercises.
By the end of this course, students will learn the mathematical basis required for understanding Earth and planetary sciences including:
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
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
---|---|---|---|---|
- | - | ✔ | - | - |
In each class, students are given a systematic explanation about the topic of the day during the first half of the class and do exercises during the last half of the class. Although there are no specific assignments, students are required to answer a quiz every class, which is used to evaluate the understanding level.
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 | Vector analysis for cylindrical coordinates and polar coordinates | Understand vector analysis for cylindrical and polar coordinates |
Class 6 | 1st order differential equation | Understand 1st order differential equation |
Class 7 | Constant-coefficient 2nd order differential equation | Understand constant-coefficient 2nd order differential equation |
Class 8 | variable coefficient linear differential equation | Understand simultaneous differential equations |
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 boundary value problem for ordinary differential equation |
Class 14 | Laplace transform | Understand Laplace transform |
Class 15 | comprehension check | Check the understanding of this course |
While there is no specified textbook, some are suggested during the class.
Not specified.
Scores are based on the final exam and quiz at every class.
No prerequisites.
Naofumi Aso（aso[at]eps.sci.titech.ac.jp)
No regular schedule but can be arranged upon request. Please make an appointment by e-mail in advance.