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課程名稱 |
工程數學二
Engineering Mathematics(Ⅱ) |
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開課學期 |
99-2 |
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授課對象 |
工程科學及海洋工程學系 |
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授課教師 |
謝傳璋 |
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課號 |
ESOE2022 |
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課程識別碼 |
505 28120 |
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班次 |
01 |
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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 |
星期二7,8(14:20~16:20)星期四3(10:20~11:10) |
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上課地點 |
工科202工科202 |
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備註 |
本系限學號單號
限本系所學生(含輔系、雙修生)
總人數上限：56人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/992Eng_Math |
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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 |
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。 |
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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 15:00~17:00
每週四 10:00~12:00 |
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指定閱讀 |
E. Kreyszig, “ Advanced Engineering Mathematics”, John Wiley & Sons |
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參考書目 |
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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. |
期中考 |
25% |
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2. |
期中考 |
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 |
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第01週 |
02/22, 02/24 |
8. Linear algebra: matrix eigenvalue problems Eigenvalues, Eigenvectors |
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第02週 |
03/01, 03/03 |
Application of Eigenvalue problems Symmetric, skew-symmetric and orthogonal matrix |
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第03週 |
03/08, 03/10 |
Hermitian, Skew-Hermitian, Unitary matrix Similarity Matrices, Basis, Diagonalization |
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第04週 |
03/15, 03/17 |
11. Fourier series, integrals and transforms Periodic function Fourier series Function of any period |
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第05週 |
03/22, 03/24 |
Half-range Expansion Complex Fourier series Forced oscillation |
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第06週 |
03/29, 03/31 |
Approximation by Trigonometric polynomials Fourier integrals Fourier sine and cosine transforms |
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第07週 |
04/05, 04/07 |
Fourier transforms.期中考一 |
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第08週 |
04/12, 04/14 |
12. Partial differential equations Modeling: vibrating string, wave equation |
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第09週 |
04/19, 04/21 |
Separation of variables D’alembert’s solution of wave equation |
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第10週 |
04/26, 04/28 |
Heat equation: solution by Fourier series Heat equation: solution by Fourier integral and transform |
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第11週 |
05/03, 05/05 |
Two-dimensional wave equation Rectangular membrane Laplacian in Polar coordinates |
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第12週 |
05/10, 05/12 |
Circular membrane Laplace equation in Cylindrical and Spherical coordinates Solutions by Laplace transform |
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第13週 |
05/17, 05/19 |
期中考二 13 Complex Numbers Complex number. Complex plane Polar form of a complex numbers. Powers and Roots |
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第14週 |
05/24, 05/26 |
curves and region in complex plane Limit, Derivative, Analytic function Cauchy-Riemann Equation Exponential and Logarithmic function Trigonometric functions and Hyperbolic functions |
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第15週 |
05/31, 06/02 |
14 Complex Integration Line integral in the complex plane Two integration methods Cauchy-Gourset Integral Theorem |
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第16週 |
06/07, 06/09 |
Existence of Indefinite Integral Cauchy’s Integral Formula Derivative of Analytic Function |
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第17週 |
06/14, 06/16 |
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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