Differential equations 4th edition by Paul Blanchard; Robert Devaney; Glen Hall ISBN 1133388086 9781133388081

Chapter 1: First-Order Differential Equations

1. 1.1 Modeling Via Differential Equations

1. 1.2 Analytic Technique: Separation Of Variables
2. 1.3 Qualitative Technique: Slope Fields
3. 1.4 Numerical Technique: Euler’s Method
4. 1.5 Existence And Uniqueness Of Solutions
5. 1.6 Equilibria And The Phase Line
6. 1.7 Bifurcations
7. 1.8 Linear Equations
8. 1.9 Integrating Factors For Linear Equations
9. Review Exercises For Chapter 1
10. Lab 1.1 Rate of Memorization Model
11. Lab 1.2 Growth of a Population of Mold
12. Lab 1.3 Logistic Population Models with Harvesting
13. Lab 1.4 Exponential and Logistic Population Models
14. Lab 1.5 Modeling Oil Production

Chapter 2: First-Order Systems

1. 2.1 Modeling Via Systems
2. 2.2 The Geometry Of Systems
3. 2.3 The Damped Harmonic Oscillator
4. 2.4 Additional Analytic Methods For Special Systems
5. 2.5 Euler’s Method For Systems
6. 2.6 Existence And Uniqueness For Systems
7. 2.7 The Sir Model Of An Epidemic
8. 2.8 The Lorenz Equations
9. Review Exercises For Chapter 2
10. Lab 2.1 Two Magnets and a Spring
11. Lab 2.2 Cooperative and Competitive Species
12. Lab 2.3 The Harmonic Oscillator with Modified Damping
13. Lab 2.4 A Mass-Spring System with a Rubber Band
14. Lab 2.5 Active Shock Absorbers

Chapter 3: Linear Systems

1. 3.1 Properties Of Linear Systems And The Linearity Principle
2. 3.2 Straight-Line Solutions
3. 3.3 Phase Portraits For Linear Systems With Real Eigenvalues
4. 3.4 Complex Eigenvalues
5. 3.5 Special Cases: Repeated And Zero Eigenvalues
6. 3.6 Second-Order Linear Equations
7. 3.7 The Trace-Determinant Plane
8. 3.8 Linear Systems In Three Dimensions
9. Review Exercises For Chapter 3
10. Lab 3.1 Bifurcations in Linear Systems
11. Lab 3.2 RLC Circuits
12. Lab 3.3 Measuring Mass in Space
13. Lab 3.4 Exploring a Parameter Space
14. Lab 3.5 Find Your Own Harmonic Oscillator
15. Lab 3.6 A Baby Bottle Harmonic Oscillator

Chapter 4: Forcing And Resonance

1. 4.1 Forced Harmonic Oscillators
2. 4.2 Sinusoidal Forcing
3. 4.3 Undamped Forcing And Resonance
4. 4.4 Amplitude And Phase Of The Steady State
5. 4.5 The Tacoma Narrows Bridge
6. Review Exercises For Chapter 4
7. Lab 4.1 Two Magnets and a Spring Revisited
8. Lab 4.2 A Periodically Forced RLC Circuit
9. Lab 4.3 The Tacoma Narrows Bridge

Chapter 5: Nonlinear Systems

1. 5.1 Equilibrium Point Analysis
2. 5.2 Qualitative Analysis
3. 5.3 Hamiltonian Systems
4. 5.4 Dissipative Systems
5. 5.5 Nonlinear Systems In Three Dimensions
6. 5.6 Periodic Forcing Of Nonlinear Systems And Chaos
7. Review Exercises For Chapter 5
8. Lab 5.1 Hard and Soft Springs
9. Lab 5.2 Higher Order Approximations of the Pendulum
10. Lab 5.3 A Family of Predator-Prey Equations
11. Lab 5.4 The Glider

Chapter 6: Laplace Transforms

1. 6.1 Laplace Transforms
2. 6.2 Discontinuous Functions
3. 6.3 Second-Order Equations
4. 6.4 Delta Functions And Impulse Forcing
5. 6.5 Convolutions
6. 6.6 The Qualitative Theory Of Laplace Transforms
7. Review Exercises For Chapter 6
8. Lab 6.1 Poles
9. Lab 6.2 Convolutions

Chapter 7: Numerical Methods

1. 7.1 Numerical Error In Euler’s Method
2. 7.2 Improving Euler’s Method
3. 7.3 The Runge-Kutta Method
4. 7.4 The Effects Of Finite Arithmetic
5. Review Exercises For Chapter 7
6. Lab 7.1 Errors of Numerical Approximations
7. Lab 7.2 Lost in Space

Chapter 8: Discrete Dynamical Systems

1. 8.1 The Discrete Logistic Equation
2. 8.2 Fixed Points And Periodic Points
3. 8.3 Bifurcations
4. 8.4 Chaos
5. 8.5 Chaos In The Lorenz System