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 learn 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
scalar, vector, differential equation, Fourier transform
✔ Specialist skills | ✔ Intercultural skills | Communication 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 calculus 1 | Vector analysis |
Class 2 | Vector calculus 2 | Vector derivative |
Class 3 | Vector calculus 3 | Integrals of a vector field |
Class 4 | Vector calculus 4 | Integral theorems |
Class 5 | Vector calculus 5 | Curvilinear coordinates and scale factors |
Class 6 | Vector calculus 6 | Vector calculus in curvilinear coordinates |
Class 7 | Vector calculus 7 | Matrices |
Class 8 | Differential equation 1 | 1st order differential equations |
Class 9 | Differential equation 2 | 2nd order differential equations |
Class 10 | Differential equation 3 | Higher order differential equations |
Class 11 | Fourier transform 1 | Fourier series and Fourier transform |
Class 12 | Fourier transform 2 | Delta function, power spectrum, and discrete Fourier transform |
Class 13 | Fourier transform 3 | Differential equation and Fourier transform |
Class 14 | Final exam | Comprehension check |
To enhance effective learning, students are encouraged to spend a certain length of time outside of class on preparation and review (including for assignments), as specified by the Tokyo Institute of Technology Rules on Undergraduate Learning (東京工業大学学修規程) and the Tokyo Institute of Technology Rules on Graduate Learning (東京工業大学大学院学修規程), for each class.
They should do so by referring to textbooks and other course material.
While there is no specified textbook, some could be 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.