2019 Mathematics for Physics A (EPS course)

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Academic unit or major
Undergraduate major in Earth and Planetary Sciences
Nakajima Junichi  Aso Naofumi 
Class Format
Lecture / Exercise     
Media-enhanced courses
Day/Period(Room No.)
Mon5-8(I311)  Thr5-8(I311)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
Access Index

Course description and aims

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.

Student learning outcomes

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

Competencies that will be developed

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, which is used to evaluate the understanding level.

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 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.

Reference books, course materials, etc.

Not specified.

Assessment criteria and methods

Scores are based on the final exam and quiz at every class.

Related courses

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

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

No prerequisites.

Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

Naofumi Aso(aso[at]eps.sci.titech.ac.jp)

Office hours

No regular schedule but can be arranged upon request. Please make an appointment by e-mail in advance.

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