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2025 (Current Year) Faculty Courses School of Materials and Chemical Technology Department of Materials Science and Engineering Graduate major in Materials Science and Engineering

Computational Materials Science

Academic unit or major
Graduate major in Materials Science and Engineering
Instructor(s)
Toshio Kamiya / Takao Sasagawa
Class Format
Lecture (Livestream)
Media-enhanced courses
-
Day of week/Period
(Classrooms)
1-2 Tue (G1-103 (G114)) / 1-2 Fri (G1-103 (G114))
Class
-
Course Code
MAT.C505
Number of credits
200
Course offered
2025
Offered quarter
2Q
Syllabus updated
Oct 16, 2025
Language
English

Syllabus

Course overview and goals

This course starts from explaining internal circuits and digital processing inside a computer in order to understand possible sources of numerical calculation errors. Then fundamental mathematics and representative algorithms of numerical analyses will be reviewed, which includes differentiation, integration, equation solvers, optimization, Fourier transform, linear algebra etc. It covers those applications such as molecular dynamics, first-principles quantum calculations, finite element method, and phase-field method.

Course description and aims

At the end of this course, students will be able to:
1) Understand what is going in a computer and know how to estimate possible errors in numerical calculations.
2) Understand fundamental ways of thinking how to perform differentiation, integration, optimization etc with assistance of a computer, and learn representative algorithms.
3) Learn fundamental physics and mathematics of microscopic simulations such as molecular dynamics and first-principles calculations, and understand to what problems they can be appropriately applied.
4) Learn fundamental physics and mathematics of macroscopic simulations such as finite element method and phase-field method, and understand to what problems they can be appropriately applied.

Keywords

Numerical analysis, Molecular Dynamics, First-principles calculation, Density functional theory, Electronic structure, Finite element method, Phase field method, micro-structure

Competencies

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

Class flow

Questions are accepted anytime during each class.

Course schedule/Objectives

Course schedule Objectives
Class 1

Fundamental of computer, Sources of errors

Understand the circuits and operation fundamental of computer, and possible error sources of numerical calculations
Class 2

Differential equation, Molecular dynamics, Interpolation

Understand difference method and its applications to differentiation, integration, and differential equation
Class 3

Solution of equations, Nonlinear optimization

Learn differential equation solvers, their applications, and nonlinear optimization.
Class 4

Smoothing, Linear least-squares method

Understand Smoothing, Linear least-squares method
Class 5

Solution of equations, Nonlinear optimization

Learn differential equation solvers, their applications, and nonlinear optimization.
Class 6

Fourier transformation, matrix, other applications

Understand Fourier transformation, matrix, other applications
Class 7

Review of numerical analysis

Review of numerical analysis
Class 8

First Principles Calculations

First Principles Calculations
Class 9

First Principles Calculations

First Principles Calculations
Class 10

First Principles Calculations

First Principles Calculations
Class 11

First Principles Calculations

First Principles Calculations
Class 12

First Principles Calculations

First Principles Calculations
Class 13

First Principles Calculations

First Principles Calculations
Class 14

First Principles Calculations

First Principles Calculations

Study advice (preparation and review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

Textbook will be specified at the class. Related text and materials will be distributed.

Reference books, course materials, etc.

None required

Evaluation methods and criteria

Students will be evaluated by a term-end assignments

Related courses

  • MAT.A205 ： Exercise on Information Processing
  • MAT.C310 ： Mathematical Methods for Materials Science

Prerequisites

Fundamental mathematics studies such as differential calculus, integral calculus, and linear algebra
Fundamental physics and chemistry studies such as classical dynamics and quantum mechanics