Lecture Notes in Differential Equations
Bruce Shapiro
Lecture Notes in Differential Equations

These lecture notes on differential equations are based on the author's experience teaching Math 280 and Math 351 at California State University, Northridge since 2000. The content of Math 280 is more applied (solving equations) and Math 351 is more theoretical (existence and uniqueness) but the author has attempted to integrate the material together in the notes in a logical order and selects material from each section for each class.

The subject matter is classical differential equations and many of the exciting topics that could be covered in an introductory class, such as nonlinear systems analysis, bifurcations, chaos, delay equations, and difference equations are omitted in favor of providing a solid grounding the basics.

The book features some contributed drawings that are charming and humorous.

Printed copies available at Lulu.

Front Cover
Table of Contents
Basic Concepts
A Geometric View
Separable Equations
Linear Equations
Bernoulli Equations
Exponential Relaxation
Autonomous ODES
Homogeneous Equations
Exact Equations
Integrating Factors
Picard Iteration
Existence of Solutions*
Uniqueness of Solutions*
Review of Linear Algebra
Linear Operators and Vector Spaces
Linear Eqs. w/ Const. Coefficents
Some Special Substitutions
Complex Roots
Method of Undetermined Coefficients
The Wronskian
Reduction of Order
Non-homog. Eqs.w/ Const. Coeff.
Method of Annihilators
Variation of Parameters
Harmonic Oscillations
General Existence Theory*
Higher Order Equations
Series Solutions
Regular Singularities
The Method of Frobenius
Linear Systems
The Laplace Transform
Numerical Methods
Critical Points
Table of Integrals
Table of Laplace Transforms
Summary of Methods
The book hasn't received reviews yet.