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# 10610PHYS212000
# 應用數學2 Applied Mathematics (II)

To develop a basic competence in each of the many areas of mathematics needed in undergraduate courses in physics.

## 教授
* 物理系陳柏中教授
* 物理系 521
* email: pcchen at phys.nthu.edu.tw

## 助教
* 梁珈郡
* 呂元鈞
* 梁洛威

## 課本
* Mathematical Methods in the Physical Sciences by Mary L. Boas


## 上課時間
* M2; R1R2

## 上課教室
* 物 019

## 演習
* 時間：Tuesday, Thursday 7-9pm
* 教室：物501

## 評量
* Midterm (35%):
  * Time: 11/16/2017, 8-10 am
  * Chapter 8
  * Chapter 12, excluding section 20,21,22,23.
* Final (35%):
  * Time 1/8/2018, 8-10 am
  * Chapter 13
  * Chapter 14
  * Chapter 10
* Homework + quiz (30%):
  * About 10 homeworks in total. 

## 課綱

### Part one
* 8: Ordinary Differentail Equations
* 12: Series Solutions of Differentail Equations

### Part two
* 10: Tensor Analysis
* 13: Partial Differentail Equations
* 14: Functionos of a Complex Variable

## 作業
* HW1, due on 10/2/2017.
  * Ch 8, Problem 1.7, 2.1, 2.3, 2.6, 2.21, 2.22, 3.1, 3.6, 3.13, 4.1, 4.6, 4.12.
* HW2, due on 10/12/2017.
  * Ch 8, Problem 2.14, 2.16, 2.32, 3.20, 5.2, 5.8, 5.19, 6.1, 6.4, 6.11, 6.21, 6.28.
* HW3, due on 10/19/2017.
  * Ch8, Problem 6.29, 6.34, 6.42, 7.1(a), 7.5, 7.16(a), 11.14, 11.17, 12.3, 12.11, 12.14.
* HW4, due on 10/26/2017.
  * Ch12, Problem 1.2, 2.1, 4.3, 4.4, 5.2, 5.3, 5.4, 5.11, 6.2, 7.1, 9.1, 9.12.
* HW5, due on 11/6/2017.
  * Ch12, Problem 10.3, 11.2,  12.2, 13.1, 15.1, 19.1.
  * Ch8, Problem 8.2, 8.4, 9.2, 11.7, 12.1.
* HW6, due on 11/20/2017.
  * Ch13, Problem 2.1, 2.5, 2.6, 2.14, 3.2, 3.3, 3.7, 3.10, 4.2, 4.7.
* HW7, due on 11/27/2017
  * Ch13, Problem 5.2, 5.4, 5.8, 7.4, 7.7, 7.13, 8.4, 8.7, 8.8.
* HW8, due on 12/7/2017
  * Ch 14, Problem 1.21, 2.23, 2.36, 2.46, 2.51, 2.60, 3.3, 3.17, 3.21, 3.22
* HW9, due on 12/25/2017
  * Ch 14, Problem 4.3, 4.11, 6.3, 6.6, 6.14, 6.23, 7.4, 7.23, 7.45, 7.56
* HW10, due on 1/8/2018
  * Ch 14, Problem 8.3, 9.5, 10.4
  * Ch 10, Problem 3.2, 3.9, 5.6(a),(c), 5.17, 6.7, 8.1, 8.2, 8.3

## 每週進度
* Week 1
  * [1]: 9/11/2017: ODE: introduction.
  * [2]: 9/14/2017: ODE: seperation of variables, first order liner ODE.
* Week 2
  * [3]: 9/18/2017: ODE: first order liner ODE.
  * [4]: 9/21/2017: ODE: slope field, second order liner ODE.
* Week 3
  * [5]: 9/25/2017: ODE: second order liner ODE.
  * [X]: 9/28/2017: 教師節(停課一天)
* Week 4
  * [6]: 10/2/2017: **HW1 due**, ODE: second order ODE.
  * [7]: 10/5/2017: The Dirac delta function. Green Functions.
* Week 5
  * [X]: 10/9/2017: 國慶日彈性放假
  * [8]: 10/12/2017: **HW2 due**, The Dirac delta function. Green Functions.
* Week 6
  * [9]: 10/16/2017: Series solutions. Legendre's equation.
  * [10]: 10/19/2017: **HW3 due**, Legendre's equation, Legendre series.
* Week 7
  * [11]: 10/23/2017: Associated Legendre functions, Generalized power series.
  * [12]: 10/26/2017: **HW4 due**, Bessel's equation. Graphs and zeros of Bessel functions. Recursion relations.
* Week 8
  * [13]: 10/30/2017: Orthogonality of Bessel functions
  * [14]: 11/2/2017:  PDE, Laplace's equation, Heat flow equation, Schrodinger equation.
* Week 9
  * [15]: 11/6/2017: **HW5 due**, PDE, Wave equation, Lapalce's equation in cylindrical coordinates.
  * [16]: 11/9/2017: Lapalce's equation in spherical coordinates., Poisson's equation.
* Week 10
  * [17]: 11/13/2017: Complex numbers and complex functions.
  * [18]: 11/16/2017: **Midterm**
* Week 11
  * [19]: 11/20/2017: **HW6 due**, analytical functions, contour integrals.
  * [20]: 11/23/2017: Contour integrals.
* Week 12
  * [21]: 11/27/2017: **HW7 due**, Laurent series.
  * [22]: 11/30/2017: Laurent series, the residue theorem.
* Week 13
  * [23]: 12/4/2017: Methods of finding residues.
  * [24]: 12/7/2017: **HW8 due**, Evaluation of definite integral by use of the resude theorem.
* Week 14
  * [25]: 12/11/2017: Evaluation of definite integral by use of the resude theorem.
  * [26]: 12/14/2017: The point at infinity. Conformal transformation.
* Week 15
  * [27]: 12/18/2017: Tensor.
  * [28]: 12/21/2017: Tensor.
* Week 16
  * [29]: 12/25/2017: **HW9 due**, Tensor.
  * [30]: 12/28/2017: 
* Week 17
  * [X]: 1/1/2018: 開國紀念日
  * [31]: 1/4/2018: Tensor.
* Week 18
  * [32]: 1/8/2018: **HW10 due**, **Final Exam**. 8am-10am.
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