Differential Equations and Their Applications

Chapter 1: First-Order Differential Equations
1.3 The Van Meegeren Art Forgeries
1.6 The Spread of Technological Innovations
1.11 Finding Roots of Equations by Iteration
1.12 Difference Equations, and How to Compute The Interest Due on Your Student Loans
1.13 Numerical Approximations; Euler’s Method
1.14 The Three Term Taylor Series Method
1.15 An Improved Euler Method
1.16 The Runge – Kutta Method
1.17 What To Do In Practice
Chapter 2: Second-Order Differential Equations
2.3 The Nonhomogeneous Equation
2.7 A Model for the Detection of Diabetes
2.8.3 Equal Roots, and Roots Differing by an Integer
2.11 Differential Equations with Discontinuous Right-Hand Sides
Chapter 3: Systems of Differential Equations
Chapter 4: Qualitative Theory of Differential Equations
4.5.1 L.F. Richardson’s Theory of Conflict
4.5.2 Lanchester’s Combat Models and The Battle of Iwo Jima
4.10 Predator-Prey Problems; or Why The Percentage of Sharks Caught in The Mediterranean Sea Rose Dramatically During World War I
4.11 The Principle of Competitive Exclusion in Population Biology
4.12 The Threshold Theorem of Epidemiology
4.13 A Model for The Spread of Gonorrhea