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課程概述與目標
本課程的目標是為建立大學生在機械工程的數學能力，課程內容將介紹工程數學的基本概念與範例。
課程章節
| 章節 | 章節名稱 |
| 第五章 | Vector Analysis |
| Vector fields | |
| The differential operators: dicergence, gradient, curl | |
| Line, surface, and volume integrals | |
| Integral theorems:divergence theorem,Greens theorem,and Stokes theorem | |
| Potential theory | |
| Applications | |
| 第六章 | Partial Differential Equations (PDE) |
| Method of characteristics | |
| Classification of PDEs | |
| Seperation of variables | |
| Solution of non-homogeneous problems | |
| Solution of PDE by integral transform methods | |
| Applications | |
| 第七章 | Complex Analysis |
| Analytic functions | |
| Taylor and Laurent series | |
| Cauchy integral and the residue theorem | |
| Application to stability analysis of systems | |
| Conformal mapping | |
| 第八章 | Special Function |
| Separation of variables in curvilinear oordinates | |
| Bessel functions | |
| Legendre polynomials | |
| Chebyshev polynomials | |
| 第九章 | Calculus of variations |
| Functional variation | |
| Constrained optimization | |
| Lagrange equation of motion |
課程書目
Wylie, C. R. and Barrett, L. C., Advanced Engineering Mathematics, 6th ed., McGraw-Hill, 1995.
參考書目
|
Kreszig, E., Advanced Engineering Mathematics, 9th ed., Prentice-Hall, 2006. |
|
Greenberg, M. D., Advanced Engineering Mathematics, 2nd ed., John-Wiley, 1998. |
|
Noble, B. and Daniel, J. W., Applied Linear Algebra, 3rd., Prentice-Hall, 1988. |
|
Haberman, R., Elementary Applied Partial Differential Equations, Prentice-Hall, 1987. |
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