數值分析
Numerical Method
| 節 | 週三 |
|---|---|
2 09:00–09:50 | 數值分析 YEA200（陽明） 3 節連堂 |
3 10:10–11:00 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
The research methodology of science is shifting from ‘‘theory + experiment’’ to ‘‘theory + experiment + computation’’, and people even use the term ‘‘data science’’. The numerical method is one of the most important parts of data science. To explore complex systems, engineers require computational methods since mathematical models are only rarely solvable algebraically. To enhance the problem solving skills of engineering students using an extremely powerful problem solving tool namely numerical methods. Such methods include techniques for differentiation and integration, interpolation from the known to the unknown, linear algebra underlying systems of equations, and differential equations to simulate systems. Besides, we also introduce the cryptology and the principles of machine learning.
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On completion of this course students will able to: 1. Understand numerical techniques to find the roots of non-linear equations and solution of system of linear equations. 2. Understand the difference operators and the use of interpolation. 3. Understand numerical differentiation and integration and numerical solutions of ordinary and partial differential equations. 4. Understand the cryptology and its applications. 5. Understand the principles of machine learning.
Final examinations
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| 週次 | 主題 |
|---|---|
| 第 1 週 | Introduction Preliminary Computer Science 2022/02/16 |
| 第 2 週 | Truncation Errors and the Taylor Series Solutions of Equations of One Variable (I) 2022/02/23 |
| 第 3 週 | Solutions of Equations of One Variable (II) 2022/03/02 |
| 第 4 週 | Curve Fitting 2022/03/09 |
| 第 5 週 | Splines and Piecewise Interpolations 2022/03/16 |
| 第 6 週 | Linear Regression 2022/03/23 |
| 第 6 週 | Solution of Simultaneous Linear Algebraic Equations 2022/03/23 |
| 第 7 週 | Numerical Integration 2022/03/30 |
| 第 7 週 | Solution of Simultaneous Linear Algebraic Equations 2022/03/30 |
| 第 8 週 | Numerical Differentiation and Finite Difference Methods 2022/04/06 |
| 第 8 週 | Numerical Integration 2022/04/06 |
| 第 9 週 | Boundary Value Problems Weighted Residual Methods 2022/04/13 |
| 第 9 週 | Numerical Differentiation 2022/04/13 |
| 第 10 週 | Boundary Value Problems Finite Difference Methods 2022/04/20 |
| 第 10 週 | Introduction to Finite Element Methods (I) 2022/04/20 |
| 第 11 週 | Introduction to Finite Element Methods (II) 2022/04/27 |
| 第 11 週 | Weighted Residual Methods 2022/04/27 |
| 第 12 週 | Cryptology (I) 2022/05/04 |
| 第 12 週 | Introduction to Finite Element Methods 2022/05/04 |
| 第 13 週 | Cryptology (II) 2022/05/11 |
| 第 13 週 | Cryptology and Secure Algorithms(I) 2022/05/11 |
| 第 14 週 | Cryptology and Secure Algorithms(II) Machine learning(I) 2022/05/18 |
| 第 14 週 | Machine Learning (I) 2022/05/18 |
| 第 15 週 | Machine Learning (II) 2022/05/25 |
| 第 15 週 | Machine learning(II) 2022/05/25 |
| 第 16 週 | Final Examination 2022/06/01 |
| 第 17 週 | Web-Based Learning: Python Programming Language 2022/06/08 |
| 第 18 週 | Web-Based Learning: Python Programming Language 2022/06/15 |
S. C. Chapra, Applied Numerical Methods with MATLAB for Engineers and Scientists, 3rd ed., McGraw-Hill, 2011. (高立圖書)
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