2- Separable differential equations- Dr. Noureldin

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