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.
• 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.