課程名稱 |
工程數學二 Engineering Mathematics (Ⅱ) |
開課學期 |
104-2 |
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 |
星期一3,4(10:20~12:10)星期四8(15:30~16:20) |
上課地點 |
工科203工科203 |
備註 |
各組必修。 總人數上限:56人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1042ESOE2022_02 |
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:
8. 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
11. 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
12. 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
13 Complex Numbers
Complex number. Complex plane
Polar form of a complex numbers. Powers and Roots
curves and region in complex plane
Limit, Derivative, Analytic function
Cauchy-Riemann Equation
Exponential and Logarithmic function
Trigonometric functions and Hyperbolic functions
14 Complex Integration
Line integral in the complex plane
Two integration methods
Cauchy-Gourset Integral Theorem
Existence of Indefinite Integral
Cauchy’s Integral Formula
Derivative of Analytic Function
15 Series & Residue
Sequences and Series
Taylor Series
Laurent Series
Zeros and Poles
Residues and Residue theorem
Evaluation of Real Integral
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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 |
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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. |
作業 |
25% |
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2. |
期末考 |
25% |
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3. |
期中考二 |
25% |
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4. |
期中考一 |
25% |
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週次 |
日期 |
單元主題 |
第1週 |
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7. Linear Algebra; Matrices, Vectors , Determinants: Basic concept |
第2週 |
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Matrix multiplication, Linear systems of Equation, Gauss Elimination |
第3週 |
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Linear independence , Rank of a matrix |
第4週 |
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Linear system : General properties of solutions, Inverse of a square matrix,Inverse by the Adjoint matrix; Cramer's rule |
第5週 |
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8. Linear algebra: matrix eigenvalue problems Eigenvalues, Eigenvectors |
第6週 |
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Application of Eigenvalue problems Symmetric, skew-symmetric and orthogonal matrix ,Hermitian, Skew-Hermitian, Unitary matrix |
第7週 |
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Similarity Matrices, Basis, Diagonalization |
第8週 |
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期中考一 |
第9週 |
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11. Fourier series, integrals and transforms Periodic function Fourier series Function of any period |
第10週 |
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Half-range Expansion Complex Fourier series Forced oscillation |
第11週 |
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Approximation by Trigonometric polynomials Fourier integrals Fourier sine and cosine transforms |
第12週 |
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Fourier transforms.期中考二 |
第13週 |
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12. Partial differential equations Modeling: vibrating string, wave equation |
第14週 |
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Separation of variables D’alembert’s solution of wave equation |
第15週 |
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Heat equation: solution by Fourier series Heat equation: solution by Fourier integral and transform |
第16週 |
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Two-dimensional wave equation Rectangular membrane Laplacian in Polar coordinates |
第17週 |
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Circular membrane Laplace equation in Cylindrical and Spherical coordinates Solutions by Laplace transform |
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