Chapter 1: Introduction

• Section 1.1 Modeling (notes)

  • (Examples of D fields (Here).

• Section 1.2 Solving Some (notes)

Chapter 4: Higher Order ODE

• Section 4.1 General Overview of Theory (notes)

• Section 4.2 Linear Homogeneous ODE (notes)

       (with constant coefficients)

• Section 4.3 Nonhomogeneous Linear ODE (notes)

Chapter 2: First Order ODE​

• Section 2.1 First Order Linear ODE (notes) 

• Section 2.2 Separable Variables (ODE) (notes)

• Section 2.3 miscellaneous ODEs (notes)

• Section 2.4 Examples of ODE Models (notes)

• Section 2.5 Existence and Uniqueness of Solutions (notes)

• Section 2.6 Equilibrium Solutions (notes)

• Section 2.7 Exact Equations (notes)

• Section 2.8 Numerical Solutions (notes)

  • Excel Spread Sheet (Here)

Chap 5: System of 1st Order Linear ODE

• Section 5.1 Introduction (notes)

• Section 5.2 Algebra of Matrices, (notes)

  • Determinant of Matrices (notes)

• Section 5.3 Linear Systems and Eigen Values (notes)

• Section 5.4 The Theoretical Foundation (notes)

• Section 5.5 Homogeneous Systems (notes)

                        (with Constant Coefficients)

• Section 5.6 Complex Eigenvalues (notes)

• Section 5.7 Repeated Eigenvalues (notes)

• Section 5.8 Nonhomogeneous Linear Systems (notes)

​Chapter 3: Second Order ODE 

• Section 3.1 Introduction (notes)

• Section 3.2 Homogenous Linear ODE (notes)

       (with constant coefficients)

• Section 3.3 Fundamental Set of Solutions (notes)

• Section 3.4 Repeated Roots of CE (notes)

• Section 3.5 Complex Roots of CE (notes)

• Section 3.6 Non homogeneous ODE (notes)

       (Method of Variation of Parameters)

• Section 3.7 Nonhomogeneous ODE (notes)

       (Method of Undetermined Coefficients)

• Section 3.8 Elements of Particle Dynamics (notes)

Chapter 6: The Laplace Transform

• Section 6.1 Definition of Laplace Transform (notes)

• Section 6.2 Solutions od Initial Value Problems (notes)

• Section 6.3 Step Functions and Dirac Delta (notes)

• Section 6.4 With Discontinuous Functions (notes)