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課程名稱
及課號

應用數學四 (Applied Mathematics) Phys 3002 (202 30340)

授課

Lectures

 

每週四第 7, 8, 9節 (15:30~18:20).
期中考前有8週上課, 期中考至期末考間有8週, 故共有 (8+8)*3=48 堂課.

Thursday cl.7,8,9 (15:30~18:20)
8 +1+8+1=18 weeks; [8+8] x 3 = 48 lectures

 

課程重點

Syllabus

 


1. PDE (Partial Differential Equations; Ref.2§8, Ref.1§8; 7 weeks):

  • a. Classification and modeling of differential equations
  • b. Wave motion, diffusion, gravitational potential
  • c. The D'Alembert Solution of wave equation, separation of variables, solutions of certain types of equations
  • d. *Green's function

2. Fourier Transform (Ref.3§12; Ref.1§15; 2weeks):

  • a. Convolution/deconvolution theorem, correlation theorem
  • b. Fast/finite Fourier transforms (FFT)
  • c. Wiener filtering, windowing, power spectrum
  • d. Solving differential equations (DE)

3. Matrices & Group Theory (Ref.1§3,4, Ref.2§4,5, Ref.4; 5 weeks):

  • a. Matrix: multiplication, inversion, determinants, orthogonality; Hermitian & unitary; diagonalization and eigenvalues/eigenvectors
  • b. Discrete groups & continuous groups
  • c. Generators; SU(2), SU(3) & nuclear particles
  • d. *Lorentz group; Lee group & Lee algebra

4. Computer Techniques (2 weeks):

  • a. Matlab & Mathematica
  • b. Numerical Methods (Ref.2§9; Ref.1§8.8):
    Finite-difference operators, integration & differentiation, roots of equations, initial-value, boundary-value problems, solution of ODE/PDE

 

參考書目

Reference books

(books with * are advanced)


1. Arfken, G.B., & Weber, H.-J.,
Mathematical Methods for Physicists, Harcourt / Academic Press;
ISBN: 0120598256
2. Potter, M.C., & Goldberg, J.,
Mathematical Methods, Prentice-Hall International Editions/Great Lakes Press;
ISBN: 1881018113
3. William, H.P., et al.,
Numerical Recipes in C (or Fortran), Cambridge University Press;
ISBN: 0521431085
*4. Hamermesh, M,
Group Theory and Its Applications to Physical Problems, Dover Pubns;
ISBN: 0486661814.

學期成績

計算方式

Assessment

 

The final grade will be the higher result of the following two plans. Exams are written, with a time limit of three hours.

Plan A
Plan B
I. Exercises
0%
20%
II. Mid-semester exam
50%
40%
III. Final exam
50%
40%

 


助教
Teaching Assistants


葉佳隆 (天文數學大樓8樓): yea107@gmail.com

張文軒 (天文數學大樓8樓): shuitun83023@gmail.com

與我連絡

Contact me

 

jhpw@phys.ntu.edu.tw
Room 808, Astrophysics and Mathematics Building
Tel: 33668629

Homepage: http://jhpw.phys.ntu.edu.tw

 

課後問題
時間
Question hours:

 

12:10pm ~ 1:00pm, Thursday

 

課程網站

Web site for course information:


http://jhpw.phys.ntu.edu.tw/course/am4


 


Department of Physics
National Taiwan University
No.1, Sec.4, Roosevelt Rd
Taipei, Taiwan
Tel:+886-2-33668629
Fax:+886-2-23655473


email me:
jhpw@phys.ntu.edu.tw