### 2017　Mathematics for Physics A (EPS course)

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Undergraduate major in Earth and Planetary Sciences
Instructor(s)
Nakajima Junichi
Course component(s)
Lecture / Exercise
Mode of instruction

Day/Period(Room No.)
Mon5-8(I311)  Thr5-8(I311)
Group
-
Course number
EPS.B201
Credits
4
2017
Offered quarter
1Q
Syllabus updated
2017/3/17
Lecture notes updated
-
Language used
Japanese
Access Index ### Course description and aims

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.

### Student learning outcomes

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

### Keywords

vector, scalar, differential equation, Fourier transform, Laplace transform, Gauss divergence theorem

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

### Class flow

Towards the end of class, students are given exercise problems related to what is taught on that day to solve.

### Course schedule/Required learning

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 Constant-coefficient 2nd order differential equation Understand 1st order differential equation
Class 7 simultaneous differential equations 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

None required.

None required

### Assessment criteria and methods

Students’ course scores are based on final exams and exercise problems.

### Related courses

• EPS.B210 ： Mathematics for Physics B (EPS course)

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

No prerequisites. 