Resource originally made available by CODEE on September 19, 2010
Originally published in 1992, this 368-page workbook includes a plethora of classroom ready exercises and projects for students in differential equations courses. Using an approach which closely parallels what goes on in science and engineering laboratories, this workbook provides computer experiments that amplify topics found in introductory ordinary differential equations texts. Excellent 2- and 3-D graphics illustrate the range of qualitative behavior of solutions and give compelling visual evidence of theoretical deductions and a greater understanding of the qualitative properties. The experiments are largely self-contained and are independent of any particular hardware/software platform or text.
This book is made available on this web site with permission from John Wiley and Sons, Hoboken, NJ.
Download Link: DifferentialEquationsLaboratoryWorkbook.pdf
Note: Please be aware that the file attached is quite large (approximately 170 MB). It may take some time for the file to be downloaded on your computer. The PDF file is searchable.
Plotting Orbits and Solution Curves
1.1 Direction Fields and Solution Curves
1.2 ODEs in Non Normal Form
1.3 Direction Fields and Orbits
1.4 Solvers and IVPs
Generating Atlas Plots
1.5 Generating Atlas Plots
First Order Rate Laws
1.6 Population Growth and Decay
1.7 Radioactive Decay: Carbon-14 Dating
1.8 Potassium-Argon Dating
Falling Bodies
1.9 Falling Bodies Near the Earth's Surface
1.10 Escape Velocities
Aliasing and Other Phenomena
1.11 Aliasing and Other Phenomena
Properties of Orbits and Solution Curves
2.1 Fundamentals
2.2 Sign Analysis
Equilibrium Solutions and Sensitivity
2.3 Pitchfork Bifurcation
Solutions That Escape to Infinity
2.4 Solutions That Escape to Infinity
Picard Process for Solving IVPs
2.5 Picard Process for Solving IVPs
Euler's Method for Solving IVPs
2.6 Euler's Method and Explicit Solutions
2.7 Limitations of Euler's Method
Euler Solutions to the Logistic Equation
2.8 Convergent Euler Sequences
2.9 Period Doubling and Chaos: Graphical Evidence
2.10 Period Doubling and Chaos: Theory
Linear First Order ODEs: Properties of Solutions
3.1 Superposition
3.2 Singularities
Linear First Order ODEs: Data
3.3 Dependence on Data
3.4 Bounded Input/Bounded Output
Separable ODEs: Implicit Solutions
3.5 Separable ODEs: Implicit Solutions
Nonlinear ODEs: Homogeneous Functions
3.6 Nonlinear ODEs: Homogeneous Functions
The ODE: M(x, y)dx + N(x, y)dy = 0
3.7 Planar Systems and M dx + N dy = 0
3.8 Construction of Integral Curves: The Cat
ODEs in Polar Coordinates
3.9 ODEs in Polar Coordinates
Comparison of Solutions of Two ODEs
3.10 Comparison of Solutions of Two ODEs
Harvesting a Species
3.11 Constant Rate Harvesting
3.12 Variable Rate Harvesting
3.13 Intermittent Harvesting
Salt Levels in a Brine
3.14 Linear Brine Models
3.15 Nonlinear Brine Models
Bimolecular Chemical Reactions
3.16 Quadratic Rates as Bimolecular Models
3.17 Modeling a Bimolecular Reaction
Properties of Solutions
4.1 Properties of Solutions
Constant Coefficient Linear ODEs: Undriven
4.2 Constant Coefficient Linear ODEs: Undriven
Constant Coefficient Linear ODEs: Driven
4.3 Beats and Resonance
4.4 General Driving Forces
Frequency Response Modeling
4.5 Parameter Identification
4.6 Gain and Phase Shift
Springs
4.7 Linear Springs
4.8 Hard and Soft Springs
4.9 Aging Springs
Circuits
4.10 Simple RLC Circuit
4.11 Tuning a Circuit
Portraits of Planar Systems
5.1 Portraits of Planar Systems
Autonomous Linear Systems
5.2 Gallery of Pictures
5.3 Stability
Driven Linear Systems
5.4 Driven Linear Systems
Interacting Species
5.5 Predator-Prey Models: Harvesting, Overcrowding
5.6 Competing Species
The Pendulum
5.7 The Undriven Pendulum: Linear Model
5.8 The Undriven Nonlinear Pendulum
5.9 The Driven Upended Pendulum
Duffing's Equation
5.10 Duffing's Equation
Planetary Motion
5.11 Elements of Orbital Mechanics
Stability and Lyapunov Functions
5.12 The Effect of a Perturbation
5.13 Stability and Lyapunov Functions
Cycles and Limit Cycles
5.14 The van der Pol System
5.15 Systems with Cycles and Limit Cycles
The Poincaré-Bendixson Alternatives
5.16 The Poincaré-Bendixson Alternatives
The Hopf Bifurcation
5.17 The Hopf Bifurcation
5.18 Satiable Predation: Bifurcation to a Cycle
Undriven Linear Systems
6.1 Portraits of Undriven Linear Systems
6.2 Asymptotic Behavior and Eigenelements
Driven Linear Systems
6.3 Transients, Steady States, Resonance
6.4 Coupled Oscillators
A Compartment Model: Lead in the Body
6.5 A Compartment Model: Lead in the Body
Lorenz System: Sensitivity
6.6 Inducing Chaos
6.7 Search for Cycles
Rössler System: Period-doubling
6.8 Rössler System: Sensitivity
The Rotational Stability of a Tennis Racket
6.9 The Rotational Stability of a Tennis Racket
Nonlinear Systems and Chemical Reactions
6.10 Approach to Equilibrium: Five Species
6.11 Approach to Equilibrium: Four Species
Oscillating Chemical Reactions
6.12 On/Off Oscillations: Autocatalator
6.13 Persistent Oscillations: The Oregonator
Bifurcations and Chaos in a Nonlinear Circuit
6.14 Bifurcations and Chaos in a Nonlinear Circuit