シラバス参照
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シラバス参照
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| 講義概要/Course Information |
| 科目基礎情報/General Information |
| 授業科目名 /Course title (Japanese) |
Introduction to Computational Methods in Science and Engineering | ||
|---|---|---|---|
| 英文授業科目名 /Course title (English) |
Introduction to Computational Methods in Science and Engineering | ||
| 科目番号 /Code |
INT505z | ||
| 開講年度 /Academic year |
2025年度 | 開講年次 /Year offered |
3/4 |
| 開講学期 /Semester(s) offered |
前学期 | 開講コース・課程 /Faculty offering the course |
情報理工学域 |
| 授業の方法 /Teaching method |
講義 | 単位数 /Credits |
2 |
| 科目区分 /Category |
総合文化科目 | ||
| 開講類・専攻 /Cluster/Department |
情報理工学域 | ||
| 担当教員名 /Lecturer(s) |
Hans-Georg Matuttis | ||
| 居室 /Office |
E4-721 | ||
| 公開E-mail |
hg@mce.uec.ac.jp | ||
| 授業関連Webページ /Course website |
https://webclass.cdel.uec.ac.jp | ||
| 更新日 /Last update |
2025/03/10 21:09:56 | 更新状況 /Update status |
公開中 /now open to public |
| 講義情報/Course Description |
| 主題および 達成目標（2,000文字以内） /Themes and goals（up to 2,000 letters） |
Computational methods have replaced analytical methods already in many fields of science and engineering, and their importance is still increasing. The aim of the lecture is to provide fundamental criteria for the choice of numerical methods, give an overview about some available methods in some fields, and give ideas about performance-oriented implementation for such methods. Depending on the background and interest of the auditory, some topics may be subject to changes. |
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| 前もって履修 しておくべき科目（1,000文字以内） /Prerequisites（up to 1,000 letters） |
First year Analysis and Linear Algebra, one procedural Programming Language |
| 前もって履修しておくこ とが望ましい科目（1,000文字以内） /Recommended prerequisites and preparation（up to 1,000 letters） |
無し |
| 教科書等（1,000文字以内） /Course textbooks and materials（up to 1,000 letters） |
Script can be downloaded from http://webclass.cdel.uec.ac.jp/, further reading: A. L. Garcia, Numerical Methods for Physics, Benjamin-Cummings Pub Co,1999 G.J. Borse: Numerical Methods with Matlab, International Thomson Publishing, 1997 |
| 授業内容と その進め方（2,000文字以内） /Course outline and weekly schedule（up to 2,000 letters） |
In the first half of the semester, the lectures on general topics will be cover the lesson time (90 minutes). In the second half, every student will get a project (topic will be discussed between students and lecturer), and the first half of the lesson will be lecture on more specific and specialized topics, and the second half will be dedicated to the completion of the project. 1. Introduction Interpreters and Compilers, basic MATLAB syntax, interacting with the operating system 2. More advanced Syntax Implicit loops, vector- and matrix commands 3. Stochastic Methods I a) Random numbers and direct Monte Carlo Averages and Variance; Computing Pi with random numbers and the power of Monte Carlo Methods for problems of arbitrary dimension 4. Stochastic Methods I b) Modeling Producing test data, Modeling 5. Numerical analysis I Why bother about errors; integer vs. floating point numbers, precision and rounding errors; Truncation error and strategies to reduce it 6. Graphics I 2D- and 3D-plots Basic plotting functions and not so basic methods of manipulating the graphs 7. Graphics II More complex Surfaces, overlaying graphics and textures, transparency alpha; From animated graphics to making movies -> End of first part 8. Linear Algebra I: From implicit loops to vectors and matrices How many matrix products are there, Performance and loop ordering; Norms, Matrix inversion and other matrix commands for linear algebra 9. Linear Algebra II Eigenvalue decomposition, Determinants, Landau-Order symbol for computational effort / complexity 10. Linear Algebra III: Non-square matrices Least squares fitting, singular value decomposition, condition number; Overfitting and Underfitting; Difference between fitting and interpolation 11. Stochastic Methods II: Spin Systems From Magnets to Spin systems: Frustration and physics problem with no good solution: Spin glasses, ground states, thermodynamics weights: Form importance Sampling Monte Carlo to Simulated Annealing at zero and finite Temperature 12. Stochastic Methods III: Neural networks as a foot note to spin glasses From infinite range spin glasses to nerve systems; Pattern recognition with Neural Networks; fast Fourier Transform and convoluting the input; the incremental advances from Neural Networks to Deep learning 13. Numerical Analysis II a) Types of numerical ordinary differential Equations Symplectic, non-stiff and stiff ODEs; standard methods with constant step size 14. Numerical Analysis II b) Types of numerical ordinary differential Equations From constant step size to variable step size |
| 実務経験を活かした 授業内容 (実務経験内容も含む) /Course content utilizing practical experience |
There will always be short programming examples during the lecture, so students should always have their MATLAB-environment ready for use. |
| 授業時間外の学習 （予習・復習等）（1,000文字以内） /Preparation and review outside class（up to 1,000 letters） |
Exercises will be given as homework. |
| 成績評価方法 および評価基準 （最低達成基準を含む） （1,000文字以内） /Evaluation and grading （up to 1,000 letters） |
20% Participation (including punctuality) and activity (asking meaningful questions and giving meaningful answers when asked) in the Lecture 80% Homework exercises |
| オフィスアワー： 授業相談（1,000文字以内） /Office hours（up to 1,000 letters） |
Contact me by E-Mail and we organise date and time at the earliest possible moment. |
| 学生へのメッセージ（1,000文字以内） /Message for students（up to 1,000 letters） |
A craving to work with "Object orientation" has derailed several students in 2022 in this course: This course is about algorithms (mostly floating point arrays), and the structuring and packaging of the data is irrelevant. You have to work out and implement algorithms, not play around with data structures in this course. |
| その他 /Others |
The lecture starts after the the introduction to the computer system in the JUSST-Program has been held. |
| キーワード /Keywords |
Numerical Analysis, Scientific Programming, Computational Science |