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工程數學 - 微分方程
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工程數學 - 微分方程


(1) 一階微分方程的解法和應用
(2) 高階微分方程的解法和應用
(3) 微分方程的級數解
(4) 拉普拉斯轉換
(5) 傅立葉級數與傅立葉轉換
(6) 偏微分方程

本課程共 30 講,包含:
影片檔 30 個   教材檔 12 個   課程回饋

單元 1.Chap. 1 Introduction to Differential Equations

內容:Chap. 1 Introduction to Differential Equations   下載影音檔 [NTU video]
單元 2.Sections 2-1 and 2-6, Solution Curves and A Numerical Method
單元 3.Sections 2-2 and 2-3 Separable Variables and Linear Equations
單元 4.Section 2-3 Linear Equations
單元 5.Chap. 3 Modeling with 1st Orer Differential Equations
單元 6.Section 2-4 Exact Equations
單元 7.Sections 2-4 and 2-5 Exact Equations and Solutions by Substitutions
單元 8.Section 4-1 Preliminary Theory for Linear Higher Order Differential Equations
單元 9.Section 4-2 Reduction of Order
單元 10.Sections 4-3 and 4-4 Solving the Linear and Constant Coefficient DE
單元 11.Section 4-5 Annilator Approach
單元 12.Sections 4-6 and 4-7 Variation of Parameters and Cauchy-Euler Equation
單元 13.Section 5-1 Applications of Linear DE
單元 14.Sections 4-9 and 4-10 Systems of Linear DEs; Nonlinear DEs
單元 15.Section 5-3 Nonlinear Models
單元 16.Chap. 8 Systems of Linear First-Order Differential Equations
單元 17.Sections 6-1 and 6-2 Review of Power Series and Solutions About Ordinary Points
單元 18.Section 6-2 Solutions about Ordinary Points
單元 19.Sections 6-3 and 6-4 Solutions About Singular Points
單元 20.Section 7-1 Definition of the Laplace Transform
單元 21.Sections 7-2 and 7-3 Inverse Laplace Transforms and Properties of Laplace Transforms (I)
單元 22.Section 7-4 Properties of Laplace Transforms (II)
單元 23.Sections 7-5 and 7-6 The Dirac Delta Function and Systems of Linear DEs
單元 24.Section 11-1 Orthogonal Functions
單元 25.Sections 11-2 and 11-3 Fourier Series, Fourier Cosine and Sine Series
單元 26.Section 11-3 Fourier Cosine and Sine Series
單元 27.Sections 14-3 and 14-4 Fourier Integral and Fourier Transforms
單元 28.Section 14-4 Fourier Transforms
單元 29.Sections 12-1, 12-2, 12-4 Separation of Variables for Solving Partial Differential
單元 30.Section 12-5 Laplace’s Equation