Lecture Notes in Differential Equations

Lecture Notes in Differential Equations

By Bruce Shapiro
Book Description

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.

Table of Contents
  • Front Cover
  • Table of Contents
  • Preface
  • 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
  • Bibliography
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