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化學數學(一) The Mathematics for Chemists (I) (Fall Term, 2006) Department of Chemistry National Sun Yat-sen University.

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Presentation on theme: "化學數學(一) The Mathematics for Chemists (I) (Fall Term, 2006) Department of Chemistry National Sun Yat-sen University."— Presentation transcript:

1 化學數學(一) The Mathematics for Chemists (I) (Fall Term, 2006) Department of Chemistry National Sun Yat-sen University

2 Campus phone:3917, Office: 理東4022 ding@mail.nsysu.edu.tw
老師 The Professor Dr. Shangwu Ding 丁尚武 Campus phone:3917, Office: 理東4022 助教 The Teaching Assistants 柯志正,劉志忠,楊威源,呂國榮,陳彥文 校內分機:3917, 理東4022 班代 Class Representative 校內分機: 手機: 請隨時向老師、助教及班代提出疑問、意見、建議

3 Lecture Hours: 09:00 am-10:00 am, Tuesdays; 14:00 pm-16:00 pm, Thursdays. (理東3001), begins from Sept 19,2006. Office Hours: 2:00-5:00 pm, Wednesdays (理東4022)

4 Instantaneous Rate of Reaction
A+2B3C+D v is the same for all species in a reaction.

5 .. Schrodinger Equation Erwin Schroedinger Operator (算子/算符)

6 2p Orbitals Nodal plane

7 Many-Electron Atoms Orbital approximation

8 Self-Consistent Field Orbitals (Hartree-Fock Technique)
Coulomb operator Exchange operator

9 General Relation of Uncertainty
Wiener Heisenberg

10 Deriving an equation of state
Derive the expression for the pressure of a gas of independent particles For a gas of independent particles: Where following relations have been used:

11 The C6H6 Molecule

12 How can we find the individual components in a signal?

13 Electronic Flow How many closed paths (for electronic flow) are there in each molecule?

14 Proteins

15 化學數學(一) [Mathematical Chemistry I],3 學分。
學會化學領域的一些較高等的數學工具,掌握用電腦程式FORTRAN解決基本的化學問題, 顯示原子、分子結構及運動等。貫穿整個課程每一章節的是公式推導和編寫程式以解決化學相關的問題。 0. 預備(Calculus, series, programming)) 數學分析回顧:微積分,級數展開 計算機程式基礎:FORTRAN,數值計算 1. 代數基礎 (Algebra) 向量(Vector) 矩陣,算子(Matrix, operator) 座標變換(Coordinate transform) 張量簡介(Tensor) 2. 群論(現已單列"群論"課程)。 分子的對稱性, 分子群的表示法, 群的基本數學原理, 群論和量子理論的關係, 群論和分子光譜的關係。 3. 微分方程基礎(Differential Equations) 簡單常微分方程(Ordinary DE) 偏微分方程(Partial DE) 微分算子與矩陣的關係(Operator vs matrix) 4.實驗數據的處理(Data Processing &Analysis) 有效數字(Significant figures) 平均值、方差(Average, variance) 誤差分析,相關係數(Uncertainty, correlation) 參數擬合(Parameter fitting) 5. 特殊函數(Special Functions) 加馬(Gamma)函數 貝他(Beta)函數 厄米(Hermite)函數 勒讓德(legendre)函數 拉蓋爾(Lagurre)函數 貝塞爾(Bessel)函數 6. 積分變換(Integration Transform) 傅立業(Fourier)變換 拉普拉斯(Laplace)變換 7. 其他 (Miscellaneous) 拓撲學簡介(Topology) 微分幾何(Differential geometry) 8.計算化學簡介(本選題視時間而定是否講授) (Computational Chemistry (time allowing)) 電腦程式程式高級設計(Advance programming) 分子圖形學高階(Molecular graphics) 計算化學軟體:熱力學,分子動力學,量子化學 (Computational software)

16 Fortran Programming Any textbooks are OK.

17 Software Fortran compiler: g 77 on PC/SGI/Linux
Plot: Excel/Origin for PC, Origin for SGI

18 Textbook 教材: The Chemistry Maths Book by Erich Steiner
Oxford University Press; 1996. ISBN: 歐亞書局有限公司 方譔惟 231台北縣新店市寶橋路235巷118號5樓 TEL: FAX:

19 歐亞書局有限公司 方譔惟 231台北縣新店市寶橋路235巷118號5樓 TEL:02-8912-1188 FAX:02-8912-1166
參考書: (1) Mathematics for Physical Chemistry, 2nd edition by Robert Mortimer Publisher: Harcourt / Academic Press; 2nd edition (May 15, 1999) ISBN: | All Editions (2) Using Computers in Chemistry and Chemical Education by Theresa Julia Zielinski (Editor), Mary L. Swift Publisher: American Chemical Society; (June 1997) ISBN: 歐亞書局有限公司 方譔惟 231台北縣新店市寶橋路235巷118號5樓 TEL: FAX:

20 Web Sites FORTRAN codes and applications:
Computer programming: FORTRAN codes and applications: 高速電腦中心計算軟體: Mathematics Info: Chemistry Info Chemistry in general:

21 Schedules 0. 預備 數學分析回顧:微積分,級數展開
0. 預備 數學分析回顧:微積分,級數展開 (Calculus, Series Expansion, 1 hr) 計算機程式基礎:FORTRAN,數值計算 (Fortran Programming, Numerical Calculations, 6-8 hrs) 1. 代數基礎(Advanced Algebra) 向量,矩陣,算子 (Vector, Matrix, Operator, 2-4 hrs) 座標變換,張量簡介 (Coordinate Transform, Tensor, 2-3 hrs) 2. 群論(現已單列“群論”課程)。 分子的對稱性, 分子群的表示法, 群的基本數學原理, 群論和量子理論的關係, 群論和分子光譜的關係。 3. 微分方程基礎 (Basic Differential Equations (DE)) 簡單常微分方程 (Ordinary DE(ODE), 2-4 hrs) 偏微分方程 (Partial DE (PDE), 2 hrs) 微分算子與矩陣的關係 (Operator as Matrix, 1 hr) 4.實驗數據的處理(Data Processing &Analysis) 有效數字,平均值、方差 (Significant Figures, Average, Variance, 1 hr) 誤差分析,相關係數 (Uncertainty, Correlation, 1 hr) 參數擬合(Parameter Fitting, 1-2 hrs)

22 Schedules 5. 特殊函數(Special Functions) 加馬(Gamma)函數 (1 hr) 貝他(Beta)函數 (1 hr) 厄米(Hermite)函數 (1-2 hrs) 勒讓德(Legendre)函數 (1-2 hrs) 拉蓋爾(Lagurre)函數 (1 hr) 貝塞爾(Bessel)函數(1 hr) 6. 積分變換(Integration Transform) 傅立業(Fourier)變換 (2-4 hrs) 拉普拉斯(Laplace)變換 (1-2 hrs) 7. 其他 (Miscellaneous) 拓撲學簡介 (Topology, 1-3 hrs) 微分幾何 (Differential Geometry, 1-2 hrs) 8.計算化學簡介(本選題視時間而定是否講授)(Computational Chemistry (time allowing)) 電腦程式程式高級設計, (Advanced Programming, 1-2 hrs) 分子圖形學高階, (Molecular Graphics, 1-2 hrs) 計算化學軟體:熱力學,分子動力學,量子化學. (Computational Software, 2-6 hrs) 共計講授時間:~48小時. (48 hrs in total)

23 Instruction Techniques
1. Lecture 2. Guided reading 3. Quiz 4. Discussion

24 Grading Policy Attendance (10%) Assignments/Quizzes (25 % each)
Midterm exam (25%) Final exam (40%) One Assignment Each Week (Deadline: 12:00 am, Tuesdays)

25


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