＜概要/Course Content Summary＞
This course, taught in English, provides an introduction to Advanced Numerical Analysis(numerical methods). This course will cover main themes: direct and iterative methods for linear systems, eigenvalue analysis, interpolation and numerical integration, numerical solutions for ODEs and PDEs.
＜到達目標/Goals,Aims＞
The goals of this course are to develop an understanding of basic concepts and procedures, to develop critical thinking skills necessary for understanding research results, and to learn to recognize and avoid misinterpretations of common numerical methods. After successfully completing this course students will understand basic numerical methods and basic ideas how to do some practical calculations on PC and how to analyze numerical results.
＜授業計画/Schedule＞
（実施回/
Week）
|
（内容/
Contents）
|
（授業時間外の学習/
Assignments）
|
|
（実施回/ Week）
1
|
（内容/ Contents）
Introduction and floating point numbers
|
（授業時間外の学習/ Assignments）
review what you have learned in the class
|
|
（実施回/ Week）
2
|
（内容/ Contents）
Direct methods of solving linear equations
|
（授業時間外の学習/ Assignments）
short homework
|
|
（実施回/ Week）
3
|
（内容/ Contents）
Conditioning of linear equations
|
（授業時間外の学習/ Assignments）
review what you have learned in the class
|
|
（実施回/ Week）
4
|
（内容/ Contents）
Iterative methods of solving linear equations
|
（授業時間外の学習/ Assignments）
short homework
|
|
（実施回/ Week）
5
|
（内容/ Contents）
Conjugate gradient method
|
（授業時間外の学習/ Assignments）
review what you have learned in the class
|
|
（実施回/ Week）
6
|
（内容/ Contents）
Solution of non-linear equaitons
|
（授業時間外の学習/ Assignments）
short homework
|
|
（実施回/ Week）
7
|
（内容/ Contents）
Eigenvalue problems I
|
（授業時間外の学習/ Assignments）
review what you have learned in the class
|
|
（実施回/ Week）
8
|
（内容/ Contents）
Eigenvalue problems II
|
（授業時間外の学習/ Assignments）
short homework
|
|
（実施回/ Week）
9
|
（内容/ Contents）
Approximation of functions
|
（授業時間外の学習/ Assignments）
short homework
|
|
（実施回/ Week）
10
|
（内容/ Contents）
Numerical integration
|
（授業時間外の学習/ Assignments）
short homework
|
|
（実施回/ Week）
11
|
（内容/ Contents）
Initial value problems for ODEs I
|
（授業時間外の学習/ Assignments）
review what you have learned in the class
|
|
（実施回/ Week）
12
|
（内容/ Contents）
Initial value problems for ODEs II
|
（授業時間外の学習/ Assignments）
short homework
|
|
（実施回/ Week）
13
|
（内容/ Contents）
Finite difference methods for PDEs I
|
（授業時間外の学習/ Assignments）
review what you have learned in the class
|
|
（実施回/ Week）
14
|
（内容/ Contents）
Finite difference methods for PDEs II
|
（授業時間外の学習/ Assignments）
short homework
|
|
（実施回/ Week）
15
|
（内容/ Contents）
Final review
|
（授業時間外の学習/ Assignments）
review the whole course
|
The above is the tentative schedule and some changes may occur depending on the COVID19 situation. Additional topics may be addressed if time is available. There may be one or more quizzes during the term, particularly in the later classes. Possible changes of the schedule will be announced via DUET.
＜成績評価基準/Evaluation Criteria＞
|
Attendance， Participation， & Effort
|
30%
|
Attendance at all class meetings is required.
|
|
Homework
|
20%
|
Understanding the content of the lectures.
|
|
Quizzes & Evaluations
|
50%
|
|
The above is the tentative grading scheme, but it is subject to change.
＜テキスト/Textbook＞
Textbook(s) will not be designated. Reading and other related material will be distributed as needed.
＜参考文献/Reference Book＞
＜備考/Remarks＞
1. Advanced Engineering Mathematics， Erwin Kreyzig， Wiley. ISBN 978-0-470-64613-7， 2011
2. Analysis of Numerical Methods Eugene Isaacson， Herbert Bishop Keller， (Dover Books on Mathematics) ISBN: 978-0486680293
3. Introduction to Numerical Analysis: Second Edition (Dover Books on Mathematics)
F.B.Hildebrand， Dover Publications ISBN 978-0486653631
4. Numerical Methods for Scientists and Engineers (Dover Books on Mathematics) ISBN: 978-0486652412
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