Lessons
I will continue to edit and up date the following lecture notes (and homework), from earlier semester:
Chapter 1: Introduction
 Section 1.1
Modeling.
Some examples of
direction fields.
 Section 1.2 Solving Some
Chapter 2: First Order ODE
 Section 2.1 First Order Linear ODE.
 Section 2.2 Separable Variables (ODE)
 Section 2.3 miscellaneous ODEs
 Section 2.4 Examples of ODE Models
 Section 2.5 Existence and
Uniqueness of Solutions
 Section 2.6 Equilibrium Solutions
 Section 2.7 Exact Equations
 Section 2.8
Numerical Solutions: Euler's Method, the
Excel Spread Sheet
Chapter 3: Second Order ODE
 Section 3.1 Introduction.
 Section 3.2 Homogenous Linear ODE,
with constant coefficients.
 Section 3.3
Fundamental Set of Solutions
 Section 3.4
Repeated Roots of CE
 Section 3.5
Complex Roots of CE
 Section 3.6
Nonhomogeneous ODE: Method of Vatiation of Parameters
 Section 3.7
Nonhomogeneous ODE: Method of Undetermined Coefficients
 Section 3.8
Elements of Particle Dynamics
Chapter 4: Higher Order ODE
 Section 4.1 General Overview of
Theory
 Section 4.2 Linear Homogeneous ODE with constant coefficients
 Section 4.3
Nonhomogeneous Linear ODE
Chapter 5: System of First Order Linear ODE
 Section 5.1 Introduction
 Section 5.2 Algebra of Matrices, and
Determinant of Matrices
 Section 5.3 Linear Systems and
Eigen Values
 Section 5.4 The Theoretical
Foundation
 Section 5.5
Homogeneous Systems with Constant
Coefficients
 Section 5.6
Complex Eigenvalues
 Section 5.7
Repeated Eigenvalues
 Section 5.8
Nonhomogeneous Linear Systems
Chapter 6: The Laplace Transform
 Section 6.1
Definition of Laplace Transform
 Section 6.2
Solutions od Initial Value Problems
 Section 6.3
Step Functions and Dirac Delta
 Section 6.4
Systems with Discontinuous Functions
Other Links
 Book of Homework
 Homework Matlab
