### 應用數學University course

• 學分： (下) 3
• 課程碼： N651200
• 必/選修： 選修
• 授課語言：
• 授課教師： 陳東陽
• 課程大綱：

1. 課程名稱: 應用數學
2. 學分數: 3
3. 課程編號:
4. 授課教師: 陳東陽
5. 課程目標:

介紹比大學工程數學更進一步的內容，使其具備更深的數學理論與知識。

We introduce a number of subjects in applied mathematics that are related to the engineering modeling of science and technology. Selected topics such as integral transforms, integral equations, and calculus of variations are included. In particular, we will address applications in engineering phenomena, such as stress waves, mechanics of solids.

1. 課程內容概要:

1. Integral transforms

Fourier (sine, cosine and exponential) transforms, Laplace transform. Mellin transform, Hankel transform, convolution, Parseval relations.

1. Integral equations

relations between differential and integral equations, Green’s functions, Fredholm equation with separable kernels, Neumann series.

1. Some special functions

Bessel function, Legendre function, Hermite functions, hypergeometric functions, etc.

1. Calculus of variations

one independent variable, several independent variables, Euler equation, Lagrange multipliers, variations subject to constraints.

1. 成績計算方式:

(a) 2 mid-term exams.                                       50%

(b) 1 final exam                                                         25%

(c) home-works                            25%

1. 教科書和主要參考書
2. Hildebrand, F. B., 1965 Methods of Applied Mathematics, Prentice-Hill.
3. Hildebrand, F. B., 1976 Advanced Calculus for Applications, Prentice-Hill.
4. Arfken, G. B. and Weber, H. J., 1995 Mathematical Methods for Physicists, Academic Press.
5. Sneddon, I. N., 1972 The Use of Integral Transforms, McGraw-Hill.

1. 建議先修課程: 工程數學

10.適合修習對象: 碩博選修