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課程名稱 |
化學數學
MATHEMATICS FOR CHEMISTS |
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開課學期 |
98-1 |
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授課對象 |
理學院 化學系 |
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授課教師 |
陳逸聰 |
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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 |
普205普205 |
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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：60人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/981math4chem |
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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 I Mathematics for Chemists I
1. 教科書:
書名:“Advanced Engineering Mathematics” 9th edition
作者:Erwin Kreyszig
出版社:John Wiley & Sons. Inc. (2006)
2. 評分方式:
Exercise 20% or 30%
Midterm exam 40% or 35%
Final exam 40% or 35%
3. 先修科目:
Calculus I, II
4. 課程綱要:
常微分方程，偏微分方程，線性代數，簡單特殊函數，變分學。
Ordinary differential equations, Partial differential equations, Linear algebra, Special functions, Calculus of variation.
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課程目標 |
PART A. Ordinary Differential Equations (ODEs)
1. First-Order ODEs
1.1 Basic Concepts.
1.2 Geometrical Meaning of y’= f(x,y). Direction Fields
1.3 Separable ODEs
1.4 Exact ODEs. Integrating Factors
1.5 Linear ODEs. Bernoulli Equation. Population Dynamics
1.7 Existence and Uniqueness of Solutions.
2. Second-Order Linear ODEs
2.1 Homogeneous Linear ODEs of Second Order
2.2 Homogeneous Linear ODEs with Constant Coefficients
2.3 Differential Operators
2.4 Modeling: Free Oscillations (Mass-Spring System)
2.5 Euler-Cauchy Equation
2.6 Existence and Uniqueness Theory. Wronskian
2.7 Nonhomogeneous ODEs
2.8 Modeling: Forced Oscillations. Resonance
2.9 Modeling: Electric Circuits
2.10 Solution by Variation of Parameters
3. Higher-Order Linear ODEs
3.1 Homogeneous Linear ODEs
3.2 Homogeneous Linear ODEs with Constant Coefficients
3.3 Nonhomogeneous Linear ODEs
4. Systems of ODEs. Phase Plane. Qualitative Methods
4.0 Basics of Matrices and Vectors
4.1 Systems of ODEs as Models
5. Series Solutions of ODEs. Special Functions
5.1 Power Series Method
5.2 Theory of the Power Series Method
5.3 Legendre’s Equation. Legendre Polynomials Pn(x)
5.4 Frobenius Method
5.5 Bessel’s Equation. Bessel Functions Jv(x)
5.6 Bessel Functions of the Second King Yv(x)
5.7 Sturm-Liouville Problems. Orthogonal Functions
PART B. Linear Algebra. Vector Calculus
7. Linear Algebra: Matrices, Vectors, Determinants. Linear Systems
7.1 Matrices, Vectors : Addition and Scalar Multiplication
7.2 Matrix Multiplication
7.3 Linear Systems of Equations. Gauss Elimination
7.4 Linear Independence. Rank of a Matrix. Vector Space
7.5 Solutions of Linear Systems: Existence, Uniqueness
7.6 For Reference: Second- and Third-Order Determinants
7.7 Determinants. Cramer’s Rule
7.8 Inverse of a Matrix. Gauss-Jordan Elimination
9. Vector Differential Calculus. Grad, Div, Curl
9.1 Vectors in 2-Space and 3-Space
9.2 Inner Product (Dot Product)
9.3 Vector Product (Cross Product)
9.4 Vector and Scalar Functions and Fields. Derivatives
9.5 Curves. Arc Length. Curvature. Torsion
9.7 Gradient of a Scalar Field. Directional Derivative
9.8 Divergence of a Vector Field
9.9 Curl of a Vector Field
PART C. Fourier Analysis. Partial Differential Equations (PDEs)
11. Fourier Series, Integrals, and Transforms (optional)
11.1 Fourier Series
11.2 Functions of Any Period p = 2L
11.3 Even and Odd Functions. Half-Range Expansions
11.5 Forced Oscillations
11.6 Approximation by Trigonometric Polynomials
11.7 Fourier Integral
11.8 Fourier Cosine and Sine Transforms
11.9 Fourier Transform. Discrete and Fast Fourier Transforms
11.10 Table of Transforms |
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課程要求 |
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預期每週課後學習時數 |
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Office Hours |
每週一 08:10~10:00
每週三 08:10~10:00 |
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指定閱讀 |
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參考書目 |
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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第1週 |
9/15,9/18 |
1-1 |
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第2週 |
9/22,9/25 |
1-1,1-2,1-3 |
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第9週 |
11/10,11/13 |
mid-term |
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第18週 |
1/12 |
final-term |
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