|
課程名稱 |
化學數學
Mathematics for Chemists |
|
開課學期 |
111-1 |
|
授課對象 |
理學院 化學系 |
|
授課教師 |
鄭原忠 |
|
課號 |
Chem2003 |
|
課程識別碼 |
203 20110 |
|
班次 |
|
|
學分 |
3.0 |
|
全/半年 |
半年 |
|
必/選修 |
選修 |
|
上課時間 |
星期三7,8,9(14:20~17:20) |
|
上課地點 |
化217 |
|
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：60人 |
|
|
|
|
課程簡介影片 |
|
|
核心能力關聯 |
核心能力與課程規劃關聯圖 |
|
課程大綱
|
|
為確保您我的權利,請尊重智慧財產權及不得非法影印
|
|
課程概述 |
9/22 Introductions and Placement Exam
9/29 High-School Review and Vector Spaces
10/6 Inner Product Spaces (Orthogonality, Projection, Completeness) and Hilbert Space
10/13 Matrices (including Special Matrices) and Determinants (including Cramer's rule)
10/20 Systems of Linear Equations and Least Squares
10/27 Eigenvalue Problem
11/3 Diagonalization, Simultaneous Diagonalization, Function of a Matrix
11/10 Linear Transformation and Basis Transformation
11/17 Dirac Delta Function, Linear Operator, Operator in Hilbert Space
11/24 期中考週
12/1 Hermitian Operator, Commutation, Uncertainty Principle
12/8 Overview of ODE, First-Order ODE, Chemical Kinetics
12/15 Second-Order Linear ODE I (homogeneous), Damped Harmonic Oscillator, Quantum Two-Level System
12/22 Second-Order Linear ODE II (non-homogeneous), Forced Harmonic Oscillator, Quantum Harmonic Oscillator
12/29 Systems of Linear ODEs, Normal Modes
1/5 Perturbation Theory, Variation Method, Molecular Orbital Theory
1/12 期末考周 |
|
課程目標 |
讓學生了解進階數學的基本原理以及在化學領域常用到的數學技巧，包括線性代數、微分方程、算符、數值方法，特別是在物理化學、無機化學、分析化學相關領域之應用。 |
|
課程要求 |
1. 總共有 15 周的課程 （每周 3 小時 + 1 小時），課堂不點名。
2. 總計有六到十次課堂作業。。
3. 評分方式為
o 課堂作業 25%
o 期中考 35%
o 期末考 40% |
|
預期每週課後學習時數 |
|
|
Office Hours |
|
|
指定閱讀 |
|
|
參考書目 |
1. M. C. Jain, “Vector Spaces and Matrices in Physics”.
2. Ramamurti Shankar, “Principles of Quantum Mechanics”
3. David J. Griffiths, “Introduction to Quantum Mechanics”
4. J. J. Sakurai, “Modern Quantum Mechanics”
5. 莊紹容 楊精松, “高等工程數學”
6. Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence, “Linear Algebra”
7. Gilbert Strang, “Differential Equations and Linear Algebra”
8. M. Levitus, “Mathematical Methods in Chemistry”:
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book%3A_Mathematical_Methods_in_Chemistry_(Levitus)
9. M. Gedalin, “Mathematical methods for physicists: A concise introduction”
http://www.freescience.info/go.php?pagename=books&id=1952 |
|
評量方式
(僅供參考) |
|
|