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8- The Non-homogeneous Equation-Variation of Parameters

Course Description (based on O'Neil textbook): INTRODUCTION CHAPTER 1 First-Order Differential Equations 1.1 Terminology and Separable Equations 1.2 Linear Equations 1.3 Exact Equations 1.4 Homogeneous and Bernoulli Equations 1.4.1 The Homogeneous Differential Equation 1.4.2 The Bernoulli Equation CHAPTER 2 Linear Second-Order Equations 2.1 The Linear Second-Order Equation 2.2 The Constant Coefficient Case 2.3 The Nonhomogeneous Equation 2.3.1 Variation of Parameters 2.3.2 Undetermined Coefficients 2.3.3 The Principle of Superposition 2.4 Spring Motion 2.4.1 Unforced Motion 2.4.2 Forced Motion 2.4.3 Resonance 2.5 Euler’s Differential Equation CHAPTER 3 The Laplace Transform 3.1 Definition and Notation 3.2 Solution of Initial Value Problems 3.3 Shifting and the Heaviside Function 3.3.1 The First Shifting Theorem 3.3.2 The Heaviside Function and Pulses 3.3.3 Heaviside’s Formula 3.4 Convolution 3.6 Solution of Systems CHAPTER 7 Matrices and Linear Systems 7.1 Matrices 7.1.1 Matrix Multiplication from another perspective 7.1.2 Terminology and Special Matrices 7.2 Elementary Row Operations 7.3 Reduced Row Echelon Form 7.5 Homogeneous Systems 7.6 Nonhomogeneous Systems 7.7 Matrix Inverses CHAPTER 8 Determinants 8.1 Definition of the Determinant 8.2 Evaluation of Determinants I 8.3 Evaluation of Determinants II 8.4 A Determinant Formula for A-1 8.5 Cramer’s Rule Introduction to Eigenvalues and Eigenvectors CHAPTER 13 Fourier Series (Introduction only) 13.1 Why Fourier Series? 13.2 The Fourier Series of a Function Main Text Books: Advanced Engineering Mathematics, by O'Neil, 7th edition Other books for reading: Advanced Engineering Mathematics, 9th ed. by E. Kreyszig Keywords: Advanced Engineering Mathematics course, Advanced Mathematics for Engineers, Ordinary Differential Equation, Mathematics class, online class mathematics, SKKU Math class, GEDB004-51, Dr. Noureldin, Dr. Mohamed Noureldin, SKKU, Advanced Engineering Mathematics, O'Neil, Kreyszig, First-Order Differential Equations, Linear Equations, Exact Equations, Homogeneous Differential Equation, Bernoulli Equation, Resonance, Euler’s Differential Equation, The Laplace Transform, Initial Value Problems, Shifting and the Heaviside Function, First Shifting Theorem, Convolution, Matrices, Nonhomogeneous Systems, Cramer’s Rule, to Eigenvalues and Eigenvectors, Fourier Series