課程資訊

MATHEMATICS FOR CHEMISTS

99-1

Chem2003

203 20110

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/991chem_math_1

M. Boas:
Mathematical Methods in the Physical Sciences
3rd Ed. Wiley, 2005
2. 評分方式:
Exercise 30%
Midterm exam 35%
Final exam 35%

3. 先修科目:
Calculus I, II
4. 課程綱要:

Ordinary differential equations, Partial differential equations, Linear algebra, Special functions, Calculus of variation.

(1 week)
Complex Number
2.6-2.11 Complex infinite series, Euler formula (standing waves and propagating waves)

(3 weeks)
Linear Algebra
3.7-3.12, 3.14 Linear vector space, Linear operators and Matrices, Eigenvalues and Eigenvectors, vibration normal modes.

(2 weeks?)
Fourier Series and Transforms
7.1-7.7 Fourier series
7.11 Parseval's theorem
7.12 Fourier transform
(Application: FTIR, X-ray form factor/structure factor)

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(2 weeks?)
Partial Differentiation
4.3 total differential
4.5-4.7 chain rule

4.8-4.9 Maximum and minimum problems with constraints
4.11 Change of variables (del^2 in spherical coordinate)

(1 week)
Calculus of Variations
9.1-9.2 Euler equation
Minimum average energy and the time-independent Schrodinger equation

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(3 weeks)
Ordinary Differential Equations
8.1-8.6
Stimulated transition of the particle in a box
12.22 operator method

(2 weeks)
Partial Differential Equations
13.1-13.4

(2 weeks)
Series Solutions of Differential Equations (Legendre, Hermite, Laguerre functions)
12.1-12.11 Legendre function, generating function, complete sets of orthogonal functions, Frobenius method
(12.21 Fuchs's theorem)

Office Hours

(僅供參考)

 No. 項目 百分比 說明 1. 期中考 33% 2. 期末考 33% 3. 平時成績 34%

 課程進度
 週次 日期 單元主題 第1週 9/15,9/17 2. Complex numbers sec.2.6-2.9, 2.11 習題：p.61 (1)(2) 第2週 9/24 2.16 (harmonic oscillator with damping) Linear algebra 3.7 習題: p.130 (12) 第3週 9/29,10/01 3.7 習題：p.131(19) p.132 (31) 3.8 習題：136 (16) 第4週 10/06,10/08 3.6 (p.121) 習題：p.122(6) p.123 (32) 3.8 習題：137 (23) 3.9 習題：p.142 (25) 第5週 10/13,10/15 3.10 習題：p.147 (4) 3.11 習題：p.160 (43) p.161 (57) 第6週 10/20,10/22 3.12 習題：p.172 (22) 第7週 10/27,10/29 3.14 習題：p.184 (4) (15) p.608 (22.13)(22.15) p. 609 (22.20) p.610 (22.22) 7.5 習題：p.355 (7) 7.7 習題：p.360 (12)(13) 7.11 第8週 11/03,11/05 作業有兩題: p294 (1); p295 (17); <11/19 才交> 第9週 11/10,11/12 no homework 第10週 11/17,11/19 老師11/17那天在黑板上出的兩題...沒有抄到的請跟同學借來看或來辦公室找我...因為題目內有方程式跟一些數學符號我不方便直接寫在這裡^^ 第11週 11/24,11/26 no homework 第12週 12/01,12/03 12.22 習題: p.612 (10) 第13週 12/08,12/10 no homework 第14週 12/15,12/17 12/17 老師寫在黑板上 求極值條件 只有一題 第17週 1/05,1/07 rotation symmetry and L, spherical coordinate expression for L, (不考 [Lx,Ly], [Lz,L+], operator method for L）更正：年輕就決鬥死亡的不是Sophus Lie http://en.wikipedia.org/wiki/Sophus_Lie