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課程名稱 |
化學數學
Mathematics for Chemists |
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開課學期 |
100-1 |
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授課對象 |
理學院 化學系 |
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授課教師 |
陸駿逸 |
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課號 |
Chem2003 |
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課程識別碼 |
203 20110 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
必帶 |
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上課時間 |
星期二3,4(10:20~12:10)星期五2(9:10~10:00) |
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上課地點 |
化210室化210室 |
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備註 |
本課程中文授課,使用英文教科書。
限學士班二年級以上 且 限本系所學生(含輔系、雙修生)
總人數上限：72人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1001ChemMath |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
化學數學 Mathematics for Chemists
課程綱要:
一、向量空間概念(Basic concept in vector space)
二、矩陣、行列式與線性聯立方程式(Matrices, determinants and systems of linear equations)
三、本徵值問題與極值問題(The eigenvalue problem and the extremal property of the quadratic forms)
四、常微分方程(含化學反應動力學的應用) (Ordinary differential equations with applications in chemical kinetics)
五、傅立葉級數(Fourier series)
六、偏微分方程(Partial differential equations)
七、群的概念與對稱群(Group, symmetry groups)
八、群的表現理論(Representations of groups)
九、群論在化學上的應用（Chemical applications of the group theory)
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課程目標 |
介紹物理化學將會遇到的數學問題。教授需要的數學關念與知識。
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課程要求 |
先修科目:
Calculus I, II |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
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參考書目 |
C. L. Perrin: Mthematics for Chemists
M. Boas: Mathematical Methods in the Physical Sciences
F.A. Cotton: Chemical Applications of Group Theory (chapters 1-6) |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Exercise |
30% |
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2. |
Midterm exam |
35% |
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3. |
Final exam |
35% |
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週次 |
日期 |
單元主題 |
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第1週 |
9/13,9/16 |
vector space, linear combination, linear independent, dimension, bases |
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第2週 |
9/20,9/23 |
coordinates, norm, inner product (real and complex versions),Dirac notation, examples of inner products |
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第3週 |
9/27,9/30 |
examples of inner product, Gram-Schmidt process, linear operator, build a matrix from a linear operator |
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第4週 |
10/04,10/07 |
linear operators and matrices, unitary matrix, orthogonal matrix, coordinate transform |
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第5週 |
10/11,10/14 |
coordinate transformation, similar matrices, eigenvalue, eigenvector |
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第6週 |
10/18,10/21 |
hermitian matrix, real eigenvalue property, orthogonal relation between the eigenvectors, simultaneous diagonalization of two hermitian matrices |
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第7週 |
10/25,10/28 |
The extremal problem of the quadratic form for hermitian matrix |
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第8週 |
11/01,11/04 |
applications in the coupled linear differential equation |
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第10週 |
11/15,11/18 |
Fourier series |
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第11週 |
11/22,11/25 |
Fourier transform, Dirac delta function |
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第14週 |
12/13,12/16 |
definition of group, group table, subgroup, conjugate elements, equivalent class |
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第15週 |
12/20,12/23 |
Symmetry group, representation |
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第16週 |
12/27,12/30 |
trace, character, product of representations, application to MO, application to IR selection rule |
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