大學課程

本課程是由交通大學機械工程系提供。

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。


授課教師　 機械工程系 白明憲教授

授課時數　 每週3小時　 共十八週


授課學分　 3學分

授課學年　 97學年度

授課對象　 大學二年級學生

預備知識　 微積分

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, CR and Barrett, LC, Advanced Engineering Mathematics, 6th ed., McGraw-Hill, 1995.

參考書目

Kreszig, E., Advanced Engineering Mathematics, 9th ed., Prentice-Hall, 2006.
Greenberg, MD, Advanced Engineering Mathematics, 2nd ed., John-Wiley, 1998.
Noble, B. and Daniel, JW, Applied Linear Algebra, 3rd., Prentice-Hall, 1988.
Haberman, R., Elementary Applied Partial Differential Equations, Prentice-Hall, 1987.