Satya Mandal

Lessons

Chapter 1: Introduction

1. Section 1.1 Modeling.  
   Some examples of direction fields.
2. Section 1.2 Solving Some

Chapter 2: First Order ODE

1. Section 2.1 First Order Linear ODE.
2. Section 2.2 Separable Variables (ODE)
3. Section 2.3 miscellaneous ODEs
4. Section 2.4 Examples of ODE Models
5. Section 2.5 Existence and Uniqueness of Solutions
6. Section 2.6 Equilibrium Solutions
7. Section 2.7 Exact Equations
8. Section 2.8 Numerical Solutions: Euler's Method, the
   Excel Spread Sheet

Chapter 3: Second Order ODE

1. Section 3.1 Introduction.
2. Section 3.2 Homogenous Linear ODE, with constant coefficients.
3. Section 3.3 Fundamental Set of Solutions
4. Section 3.4 Repeated Roots of CE
5. Section 3.5 Complex Roots of CE
6. Section 3.6 Nonhomogeneous ODE: Method of Vatiation of Parameters
7. Section 3.7 Nonhomogeneous ODE: Method of Undetermined Coefficients
8. Section 3.8 Elements of Particle Dynamics

Chapter 4: Higher Order ODE

1. Section 4.1 General Overview of Theory
2. Section 4.2 Linear Homogeneous ODE with constant coefficients
3. Section 4.3 Nonhomogeneous Linear ODE

Chapter 5: System of First Order Linear ODE

1. Section 5.1 Introduction
2. Section 5.2 Algebra of Matrices, and
   Determinant of Matrices
3. Section 5.3 Linear Systems and Eigen Values
4. Section 5.4 The Theoretical Foundation
5. Section 5.5 Homogeneous Systems with Constant Coefficients
6. Section 5.6 Complex Eigenvalues
7. Section 5.7 Repeated Eigenvalues
8. Section 5.8 Nonhomogeneous Linear Systems

Chapter 6: The Laplace Transform

1. Section 6.1 Definition of Laplace Transform
2. Section 6.2 Solutions od Initial Value Problems
3. Section 6.3 Step Functions and Dirac Delta
4. Section 6.4 Systems with Discontinuous Functions

Other Links

1. Book of Homework

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2. Homework Matlab