Course Title : Applied Numerical Methods

Code 10G001
Course Year Master Course
Term 1st term
Class day & Period Mon 1st
Location C3-Lecture Room 1
Credits 2
Restriction No Restriction
Lecture Form(s) Lecture
Language Japanese
Instructor Toshiyuki Tsuchiya

Course Description

 Numerical techniques, such as the finite element method and numerical control method, are indispensable in mechanical engineering. In this lecture, basics of numerical techniques which are required to study advanced methods for graduated students will be explained. The lecture will cover the linear system solution (Ax=b), eigenvalue analysis, interpolation approximation method, solutions of ordinary differential equation and partial differential equation. The programing exercise is included in this lecture.

Grading

Home works (four home works will be assigned) and examination.

Course Goals

Understandings of mathematical theories and programing implementations of the numerical methods.

Course Topics

Theme Class number of times Description
Introduction 1 Introduction of this class
Numerical representations and errors
Macro programing using spread sheet applications
Linear system 1 Matrix
Norms
Singular value decomposition
Linear simultaneous equation 1 2 Solution of simultaneous linear equations
direct method, iteration method
Eigenvalue analysis 2 Eigenvalue problems
Interpolation 2 Interpolation and its errors
Numerical integral 2 Numerical integration methods
Normal differential equation and numerical integral 1 explicit method, implicit method
initial value problem, boundary value problem
Partial differential equation 3 Differential expression of partial differential
Diffusion equation, wave equation
Poisson equation, Laplace equation
Examination 1 Feedback for homework and examination

Textbook

Lecture note will be distributed through the course website.

Textbook(supplemental)

Golub, G. H. and Loan, C. F. V., Matrix Computations, John Hopkins University Press
R.D.Richtmyer and K.W.Morton, Difference Methods for Initial-Value Problems, Second Edition, John Wiley & Sons 1967

Prerequisite(s)

Basic mathematics for undergraduates
Basic macro programing

Independent Study Outside of Class

Problems are based on macro on Microsoft Excel or LibreOffice.

Web Sites

Lecture notes, home works, and other info will be distributed through PandA: https://panda.ecs.kyoto-u.ac.jp

Additional Information

Have a PC with Microsoft Excel with VBA or LibreOffice (https://ja.libreoffice.org/).