Lectures, Problems and Solutions for Ordinary Differential Equations

The following sections are included:

• Preface
• Contents

The following sections are included:

• Definition of Differential Equations
• Mathematical Models
  • Newton's Law of Cooling
  • Newton's Law of Motion
  • Torricelli's Law for Draining
  • Population Models
  • A Swimmer's Problem
  • Slope Fields & Solution Curves
• Separation of Variables
• Linear First-Order DEs
• Substitution Methods
  • Polynomial Substitution
  • Homogeneous DEs
  • Bernoulli DEs
• The Exact DEs
• Riccati DEs

The following sections are included:

• Population Model
  • General Population Equation
  • The Logistic Equation
  • Doomsday vs. Extinction
• Acceleration-Velocity Model
  • Velocity and Acceleration Models
  • Air Resistance Model
  • Gravitational Acceleration
• An Example in Finance

The following sections are included:

• Classification of DEs
• Linear Independence
• Constant Coefficient Homogeneous DEs
• Cauchy-Euler DEs
• Inhomogeneous Higher Order DEs
• Variation of Parameters

The following sections are included:

• Basics of DE systems
• First-Order Systems and Applications
• Substitution Method
• Operator Method
• Eigen-Analysis Method

The following sections are included:

• Laplace Transforms
• Properties of Laplace Transforms
  • Laplace Transforms for Polynomials
  • The Translator Property
  • Shifting Property
  • The t-multiplication property
  • Periodic Functions
  • Differentiation and Integration Property
• Inverse Laplace Transforms
• The Convolution of Two Functions
• Application of Laplace Transforms

The following sections are included:

• Appendix A: Solutions to Selected Problems
  • Chapter 1: First-Order DEs
    • Definition of DEs
    • Mathematical Models
    • Separation of Variables
    • Linear First-Order DEs
    • Substitution Methods
    • The Exact DEs
    • Riccati DEs
  • Chapter 2: Mathematical Models
    • Population Model
    • Acceleration-Velocity Model
    • An example in Finance
  • Chapter 3: Linear Des of Higher Order
    • Classification of DEs
    • Linear Independence
    • Constant Coefficient Homogeneous DEs
    • Cauchy-Euler DEs
    • Inhomogeneous Higher Order DEs
    • Variation of Parameters
  • Chapter 4: Systems of Linear DEs
    • First-Order Systems and Applications
    • Substitution Method
    • Operator Method
    • Eigen-Analysis Method
  • Chapter 5: Laplace Transforms
    • Properties of Laplace Transforms
    • Inverse Laplace Transforms
    • The Convolution of Two Functions
    • Application of Laplace Transforms
• Appendix B: Laplace Transforms
  • Selected Laplace Transforms
  • Selected Properties of Laplace Transforms
• Appendix C: Derivatives & Integrals
• Appendix D: Abbreviations
• Appendix E: Teaching Plans

The following sections are included:

• References
• Index