Lectures, Problems and Solutions for Ordinary Differential Equations

The following sections are included:

• Preface
• Contents

The following sections are included:

• Definition of Differential Equations
• Slope Fields and Solution Curves
• Separation of Variables
• First-Order Linear DEs
• The Substitution Methods
  • Polynomial Substitution
  • Homogeneous DEs
  • Bernoulli DEs
• Riccati DEs
• The Exact DEs
• Summary

The following sections are included:

• Newton’s Law of Cooling
• Torricelli’s Law for Draining
• The Population Model
  • Introduction
  • General Population Equation
  • The Logistic Equation
  • Doomsday vs. Extinction
• Acceleration-Velocity Model
  • Newton’s Laws of Motion
  • Velocity and Acceleration Models
  • Air Resistance Model
  • Gravitational Acceleration
• Windy Day Plane Landing
• A Swimmer’s Problem
• River Ferryboat-Docking Problem
• Equation For Compound Interest

The following sections are included:

• Classifications of Linear DEs
• Linear Independence
• Homogeneous DEs
  • DEs with Constant Coefficients
  • DEs with Variable Coefficients
• Inhomogeneous Linear DEs
  • Method of Undetermined Coefficients
  • Variation of Parameters

The following sections are included:

• Basics of System of DEs
• First-Order Systems and Applications
  • One Block and One Spring
  • Two Blocks and Two Springs
  • Kirchhoff Circuit Laws
• The Substitution Method
• The Operator Method
• The Eigen-Analysis Method
• Examples Of Systems Of DEs
  • Predator-prey DEs
  • Cascade of Tanks

The following sections are included:

• Laplace Transforms
• Properties Of Laplace TransformS
  • Laplace Transforms for Polynomials
  • The Translator Property
  • Transforms of Step and Delta Functions
  • The t-multiplication Property
  • Periodic Functions
  • Differentiation and Integration Property
• Inverse Laplace Transforms
• The Convolution Of Two Functions
• Applications

The following sections are included:

• Appendix A Solutions to Problems
  • Chapter 1 First-Order DEs
    • Definition of DEs
    • Slope Fields and Solution Curves
    • Separation of Variables
    • First-Order Linear DEs
    • Substitution Methods
    • Riccati DEs
    • The Exact DEs
  • Chapter 2 Mathematical Models
    • Newton’s Law of Cooling
    • Torricelli’s Law for Draining
    • Population Model
    • Acceleration-Velocity Model
    • Windy Day Plane Landing
    • A Swimmer’s Problem
    • River Ferryboat-Docking Problem
    • Equation for Compound Interest
  • Chapter 3 Linear Des of Higher Order
    • Classification of Linear DEs
    • Linear Independence
    • Homogeneous DEs
    • Inhomogeneous Linear DEs
  • Chapter 4 Systems of Linear DEs
    • Basics of System of DEs
    • First-Order Systems and Applications
    • Substitution Method
    • The Operator Method
    • The Eigen-Analysis Method
    • Examples of Systems
  • Chapter 5 Laplace Transforms
    • Properties of Laplace Transforms
    • Inverse Laplace Transforms
    • The Convolution of Two Functions
    • Applications
  • Appendix B Laplace Transforms
    • Selected Laplace Transforms
    • Selected Properties of Laplace Transforms
  • Appendix C Basic Formulas
  • Appendix D Abbreviations

The following sections are included:

• References
• Index