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
To explore complex systems, engineers require computational methods since mathematical models are only rarely solvable algebraically. 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. Such methods include techniques for differentiation and integration, interpolation from the known to the unknown, and linear algebra underlying systems of equations. Besides, we also introduce the cryptology and the machine learning fundamentals.
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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 the solution of system of linear equations. 2. Understand the difference operators and the use of interpolation. 3. Understand numerical differentiation and integration. 4. Understand the cryptology and its applications. 5. Understand the principles of machine learning.
Course attendance: 20% Midterm examination: 40% Final report: 40%
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| 週次 | 主題 |
|---|---|
| 第 1 週 | 1. Introduction 2. Preliminary Computer Science 3. Errors 2023-02-15(三) 時數：[2023-02-15]鄔蜀威(3.00) |
| 第 2 週 | 1. Taylor Series 2. Solutions of Equations of One Variable 2023-02-22(三) 時數：[2023-02-22]鄔蜀威(3.00) |
| 第 3 週 | Interpolation and Curve Fitting 2023-03-01(三) 時數：[2023-03-01]鄔蜀威(3.00) |
| 第 4 週 | Splines and Piecewise Interpolations 2023-03-08(三) 時數：[2023-03-08]鄔蜀威(3.00) |
| 第 5 週 | Solution of Simultaneous Linear Algebraic Equations 2023-03-15(三) 時數：[2023-03-15]鄔蜀威(3.00) |
| 第 6 週 | Numerical Integration 2023-03-22(三) 時數：[2023-03-22]鄔蜀威(3.00) |
| 第 7 週 | Numerical Differentiation 2023-03-29(三) 時數：[2023-03-29]鄔蜀威(3.00) |
| 第 8 週 | 1. Midterm Examination 2. Introduction to Finite Element Methods 2023-04-05(三) 時數：[2023-04-05]鄔蜀威(3.00) |
| 第 9 週 | Cryptology (I) 2023-04-12(三) 時數：[2023-04-12]鄔蜀威(3.00) |
| 第 10 週 | 1. Cryptology (II) 2. Virtual Currency and Blockchain 2023-04-19(三) 時數：[2023-04-19]鄔蜀威(3.00) |
| 第 11 週 | Introduction to Machine Learnibg 2023-04-26(三) 時數：[2023-04-26]鄔蜀威(3.00) |
| 第 12 週 | Optimization 2023-05-03(三) 時數：[2023-05-03]鄔蜀威(3.00) |
| 第 13 週 | Regression Analysis 2023-05-10(三) 時數：[2023-05-10]鄔蜀威(3.00) |
| 第 14 週 | Algorithms of Supervised Learning(I) 2023-05-17(三) 時數：[2023-05-17]鄔蜀威(3.00) |
| 第 15 週 | Algorithms of Supervised Learning(II) 2023-05-24(三) 時數：[2023-05-24]鄔蜀威(3.00) |
| 第 16 週 | Algorithms of Unsupervised Learning 2023-05-31(三) 時數：[2023-05-31]鄔蜀威(3.00) |
| 第 17 週 | Manifold Learning 2023-06-07(三) 時數：[2023-06-07]鄔蜀威(3.00) |
| 第 18 週 | Web-Based Learning: Python Programming Language 2023-06-14(三) 時數：[2023-06-14]鄔蜀威(3.00) |
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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