課程名稱 |
工程數學二 ENGINEERING MATHEMATICS(II) |
開課學期 |
98-2 |
授課對象 |
工程科學及海洋工程學系 |
授課教師 |
王昭男 |
課號 |
ESOE2022 |
課程識別碼 |
505 28120 |
班次 |
02 |
學分 |
3 |
全/半年 |
半年 |
必/選修 |
必帶 |
上課時間 |
星期二7,8(14:20~16:20)星期四3(10:20~11:10) |
上課地點 |
工科203工科203 |
備註 |
本系限學號雙號 限本系所學生(含輔系、雙修生) 總人數上限:56人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/982ENGMATH2 |
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 |
課程大綱
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課程概述 |
一、課程簡介:
6. Linear algebra: matrices, vectors, determinants
Basic concept
Matrix multiplication
Gauss elimination
Rank of a matrix
Solutions of a linear system
Determinants, Cramer’s rule
Inverse of a matrix, Gauss-Jordan elimination
Vector spaces, inner product spaces, linear transformation
7. Linear algebra: matrix eigenvalue problems
Eigenvalues, Eigenvectors
Application of Eigenvalue problems
Symmetric, skew-symmetric and orthogonal matrix
Hermitian, Skew-Hermitian, Unitary matrix
Similarity Matrices, Basis, Diagonalization
8. Fourier series, integrals and transforms
Periodic function
Fourier series
Function of any period
Half-range Expansion
Complex Fourier series
Forced oscillation
Approximation by Trigonometric polynomials
Fourier integrals
Fourier sine and cosine transforms
Fourier transforms
9. Partial differential equations
Modeling: vibrating string, wave equation
Separation of variables
D’alembert’s solution of wave equation
Heat equation: solution by Fourier series
Heat equation: solution by Fourier integral and transform
Two-dimensional wave equation
Rectangular membrane
Laplacian in Polar coordinates
Circular membrane
Laplace equation in Cylindrical and Spherical coordinates
Solutions by Laplace transform
10. Complex numbers
Complex number, complex plane
Polar form of complex numbers, powers and roots
Curves and regions in complex plane
Limit, Derivative, Analytic function
Cauchy-Riemann equation
Exponential and Logarithmic function
Trigonometric functions and Hyperbolic functions
11. Complex integral
Line integral in the complex plane
Two integration method
Cauchy-Gourset Integral Theorem
Existence of Indefinite Integral
Cauchy`s Integral Formula
Derivative of Analytic function
12. Series and Residue
Sequences and series
Tayloe series
Laurent series
Zeros and Poles
Residu |
課程目標 |
建立同學後續專業課程所需的數學模式建立及簡單數學模式求解的能力。 |
課程要求 |
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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 |
Kreyszig, E."Advanced Engineering Mathematics". John Wiley & Sons,Inc. 1993. |
參考書目 |
Kreyszig, E."Advanced Engineering Mathematics". John Wiley & Sons,Inc. 1993. |
評量方式 (僅供參考) |
No. |
項目 |
百分比 |
說明 |
1. |
期中考一 |
25% |
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2. |
期中考二 |
25% |
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3. |
期末考 |
25% |
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4. |
作業 |
25% |
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週次 |
日期 |
單元主題 |
第1週 |
2/23,2/25 |
Chapter 8 |
第2週 |
3/02,3/04 |
Chapter 9 |
第3週 |
3/09,3/11 |
Chapter 11 |
第4週 |
3/16,3/18 |
Chapter 12 |
第5週 |
3/23,3/25 |
Chapter 13 |
第6週 |
3/30,4/01 |
Chapter 14 |
第7週 |
4/06,4/08 |
Chapter 15 |
第8週 |
4/13,4/15 |
Chapter 16 |
第9週 |
4/20,4/22 |
Gibbs phenomenon |
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