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. 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.
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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.
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| 週次 | 主題 |
|---|---|
| 第 1 週 | Introduction Preliminary Computer Science |
| 第 2 週 | Truncation Errors and the Taylor Series Solutions of Equations of One Variable (I) |
| 第 3 週 | Solutions of Equations of One Variable (II) |
| 第 4 週 | Curve Fitting |
| 第 5 週 | Splines and Piecewise Interpolations |
| 第 6 週 | Linear Regression Fourier Series |
| 第 7 週 | Solution of Simultaneous Linear Algebraic Equations |
| 第 8 週 | Numerical Integration |
| 第 9 週 | Numerical Differentiation |
| 第 10 週 | Solutions of Matrix Eigenvalue |
| 第 11 週 | Boundary Value Problems Finite Difference Methods |
| 第 12 週 | Weighted Residual Methods |
| 第 13 週 | Finite Element Methods (I) |
| 第 14 週 | Finite Element Methods (II) |
| 第 15 週 | Finite Element Methods (III) |
| 第 16 週 | Final Examination |
| 第 17 週 | Web-Based Learning: Python Programming Language |
| 第 18 週 | Web-Based Learning: Python Programming Language |
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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