2024 Faculty Courses School of Science Undergraduate major in Earth and Planetary Sciences
Mathematics for Physics A (EPS course)
- Academic unit or major
- Undergraduate major in Earth and Planetary Sciences
- Instructor(s)
- Yuta Amezawa
- Class Format
- Lecture/Exercise (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-8 Mon / 5-8 Thu
- Class
- -
- Course Code
- EPS.B201
- Number of credits
- 220
- Course offered
- 2024
- Offered quarter
- 1Q
- Syllabus updated
- Mar 17, 2025
- Language
- Japanese
Syllabus
Course overview and goals
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. Students are expected to understand the basic concepts of fundamental mathematics including vector calculus, differential equations, and the Fourier transform, and to learn the mathematical skill necessary for studying Earth and planetary science. After the systematic explanation from the lecturer, students learn mathematical knowledge and skills by solving problems proactively throughout exercises.
Course description and aims
By the end of this course, students will learn the mathematical basis required for understanding Earth and planetary sciences including:
1) Vector calculus
2) Ordinary and partial differential equations
3) Fourier transform, delta function, and Green’s function
Keywords
Scalar
Vector
Matrix
Differential equation
Fourier transform
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
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, so please carefully review what you learned in each class.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Eigenvalue problem / Vector calculus 1 | Eigenvalue problem / matrix diagonalization / Vector operations |
| 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 | Vector calculus in curvilinear coordinates |
| Class 8 | Fourier transform 1 | Fourier series and Fourier transform |
| Class 9 | Fourier transform 1 | Properties of Fourier transform / Delta function / Spectrum |
| Class 10 | Differential equation 1 | 1st order ordinary differential equations |
| Class 11 | Differential equation ２ | 1st order ordinary differential equations / Higher order ordinary differential equations |
| Class 12 | Differential equation ３ | Higher order ordinary differential equations / Simultaneous ordinary differential equations |
| Class 13 | Differential equation ４ | Partial differential equations |
| Class 14 | Final exam | Comprehension check |
Study advice (preparation and review)
As the topic of each class bases on those of the previous classes, please review it after each class to prepare for the next class.
Textbook(s)
This course does not base on any specific textbook.
Reference books, course materials, etc.
A summary note is provided at each class.
Evaluation methods and criteria
Students' scores bases on quizzes in every class and the final exam.
Related courses
- EPS.B210 ： Mathematics for Physics B (EPS course)
Prerequisites
No prerequisites.
Contact information (e-mail and phone) Notice : Please replace from ”[at]” to ”@”(half-width character).
Yuta Amezawa（amezawa.y.aa[at]m.titech.ac.jp)
Office hours
Any day-time, but I preferred to make an appointment by e-mail in advance.