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by Paul Blanchard, Robert L. Devaney and Glen R. Hall

Edition: 2ND 02Copyright: 2002

Publisher: Brooks/Cole Publishing Co.

Published: 2002

International: No

Paul Blanchard, Robert L. Devaney and Glen R. Hall

Edition: 2ND 02This title is currently not available in digital format.

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The authors stress a more balanced approach, one that includes analytic, numeric, and graphical techniques. The book emphasizes modeling and qualitative theory throughout the course. It employs technology significantly and consistently, presents linear and nonlinear systems in parallel, and includes an introduction to discrete dynamical systems. This text grew out of the Boston University Differential Equations Project, funded in part by the National Science Foundation.

**Benefits: **

- Technology is used throughout the book as a tool for illustration, experimentation, and discovery. Using the computer as a tool, students investigate solutions graphically as well as analytically, which leads to a better understanding of the properties of solutions.
- This text's emphasis on interpretation, qualitative description, projects, and written explanations also leads to improvement of conceptual understanding. The chapter on discrete dynamical systems forms a connection between the topics discussed in this text and recent research in mathematics.
- NEW! This edition features improved exercise sets and several new projects, including: The Flight of a Glider, A Forced Cantilever Beam, A Simple Model of the Tacoma Narrows Bridge.
- NEW! A CD-ROM is now included free with the text, to simplify using technology in the course.

1. FIRST-ORDER DIFFERENTIAL EQUATIONS.

Modeling via Differential Equations. Analytic Technique: Separation of Variables. Qualitative Technique: Slope Fields. Numerical Technique: Euler's Method. Existence and Uniqueness of Solutions. Equilibria and the Phase Line. Bifurcations. Linear Differential Equations. Changing Variables. Labs for Chapter 1.

2. FIRST-ORDER SYSTEMS.

Modeling Via Systems. The Geometry of Systems. Analytic Methods for Special Systems. Euler's Method for Systems. Qualitative Analysis. The Lorenz Equations. Labs for Chapter 2.

3. LINEAR SYSTEMS.

Properties of Linear Systems and the Linearity Principle. Straight-Line Solutions. Phase Planes for Linear Systems with Real Eigenvalues. Complex Eigenvalues. The Special Cases: Repeated and Zero Eigenvalues. Second-Order Linear Equations. The Trace-Determinant Plane. Linear Systems in Three Dimensions. Labs for Chapter 3.

4. FORCING AND RESONANCE.

Forced Harmonic Oscillators. Sinusoidal Forcing and Resonance. Undamped Forcing and Resonance. Quantitative Analysis of the Forced Harmonic Analysis. The Tacoma Narrows Bridge. Labs for Chapter 4.

5. NONLINEAR SYSTEMS.

Equilibrium Point Analysis. Qualitative Analysis. Hamiltonian Systems. Dissipative Systems. Nonlinear Systems in Three Dimensions. Labs for Chapter 5.

6. LAPLACE TRANSFORMS.

Laplace Transforms. Discontinuous Functions. Second-Order Equations. Delta Functions and Impulse Forcing. Convolutions. The Qualitative Theory of Laplace Transforms. Labs for Chapter 6.

7. NUMERICAL METHODS.

Numerical Error in Euler's Method. Improving Euler's Method. The Runge-Kutta Method. The Effects of Finite Arithmetic. Labs for Chapter 7.

8. DISCRETE DYNAMICAL SYSTEMS.

The Discrete Logistic Equation. Fixed and Periodic Points. Bifurcations. Chaos. Chaos in the Lorenz System. Labs for Chapter 8.

HINTS AND ANSWERS.

INDEX.

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Summary

The authors stress a more balanced approach, one that includes analytic, numeric, and graphical techniques. The book emphasizes modeling and qualitative theory throughout the course. It employs technology significantly and consistently, presents linear and nonlinear systems in parallel, and includes an introduction to discrete dynamical systems. This text grew out of the Boston University Differential Equations Project, funded in part by the National Science Foundation.

**Benefits: **

- Technology is used throughout the book as a tool for illustration, experimentation, and discovery. Using the computer as a tool, students investigate solutions graphically as well as analytically, which leads to a better understanding of the properties of solutions.
- This text's emphasis on interpretation, qualitative description, projects, and written explanations also leads to improvement of conceptual understanding. The chapter on discrete dynamical systems forms a connection between the topics discussed in this text and recent research in mathematics.
- NEW! This edition features improved exercise sets and several new projects, including: The Flight of a Glider, A Forced Cantilever Beam, A Simple Model of the Tacoma Narrows Bridge.
- NEW! A CD-ROM is now included free with the text, to simplify using technology in the course.

Table of Contents

1. FIRST-ORDER DIFFERENTIAL EQUATIONS.

Modeling via Differential Equations. Analytic Technique: Separation of Variables. Qualitative Technique: Slope Fields. Numerical Technique: Euler's Method. Existence and Uniqueness of Solutions. Equilibria and the Phase Line. Bifurcations. Linear Differential Equations. Changing Variables. Labs for Chapter 1.

2. FIRST-ORDER SYSTEMS.

Modeling Via Systems. The Geometry of Systems. Analytic Methods for Special Systems. Euler's Method for Systems. Qualitative Analysis. The Lorenz Equations. Labs for Chapter 2.

3. LINEAR SYSTEMS.

Properties of Linear Systems and the Linearity Principle. Straight-Line Solutions. Phase Planes for Linear Systems with Real Eigenvalues. Complex Eigenvalues. The Special Cases: Repeated and Zero Eigenvalues. Second-Order Linear Equations. The Trace-Determinant Plane. Linear Systems in Three Dimensions. Labs for Chapter 3.

4. FORCING AND RESONANCE.

Forced Harmonic Oscillators. Sinusoidal Forcing and Resonance. Undamped Forcing and Resonance. Quantitative Analysis of the Forced Harmonic Analysis. The Tacoma Narrows Bridge. Labs for Chapter 4.

5. NONLINEAR SYSTEMS.

Equilibrium Point Analysis. Qualitative Analysis. Hamiltonian Systems. Dissipative Systems. Nonlinear Systems in Three Dimensions. Labs for Chapter 5.

6. LAPLACE TRANSFORMS.

Laplace Transforms. Discontinuous Functions. Second-Order Equations. Delta Functions and Impulse Forcing. Convolutions. The Qualitative Theory of Laplace Transforms. Labs for Chapter 6.

7. NUMERICAL METHODS.

Numerical Error in Euler's Method. Improving Euler's Method. The Runge-Kutta Method. The Effects of Finite Arithmetic. Labs for Chapter 7.

8. DISCRETE DYNAMICAL SYSTEMS.

The Discrete Logistic Equation. Fixed and Periodic Points. Bifurcations. Chaos. Chaos in the Lorenz System. Labs for Chapter 8.

HINTS AND ANSWERS.

INDEX.

Publisher Info

Publisher: Brooks/Cole Publishing Co.

Published: 2002

International: No

Published: 2002

International: No

The authors stress a more balanced approach, one that includes analytic, numeric, and graphical techniques. The book emphasizes modeling and qualitative theory throughout the course. It employs technology significantly and consistently, presents linear and nonlinear systems in parallel, and includes an introduction to discrete dynamical systems. This text grew out of the Boston University Differential Equations Project, funded in part by the National Science Foundation.

**Benefits: **

- Technology is used throughout the book as a tool for illustration, experimentation, and discovery. Using the computer as a tool, students investigate solutions graphically as well as analytically, which leads to a better understanding of the properties of solutions.
- This text's emphasis on interpretation, qualitative description, projects, and written explanations also leads to improvement of conceptual understanding. The chapter on discrete dynamical systems forms a connection between the topics discussed in this text and recent research in mathematics.
- NEW! This edition features improved exercise sets and several new projects, including: The Flight of a Glider, A Forced Cantilever Beam, A Simple Model of the Tacoma Narrows Bridge.
- NEW! A CD-ROM is now included free with the text, to simplify using technology in the course.

1. FIRST-ORDER DIFFERENTIAL EQUATIONS.

Modeling via Differential Equations. Analytic Technique: Separation of Variables. Qualitative Technique: Slope Fields. Numerical Technique: Euler's Method. Existence and Uniqueness of Solutions. Equilibria and the Phase Line. Bifurcations. Linear Differential Equations. Changing Variables. Labs for Chapter 1.

2. FIRST-ORDER SYSTEMS.

Modeling Via Systems. The Geometry of Systems. Analytic Methods for Special Systems. Euler's Method for Systems. Qualitative Analysis. The Lorenz Equations. Labs for Chapter 2.

3. LINEAR SYSTEMS.

Properties of Linear Systems and the Linearity Principle. Straight-Line Solutions. Phase Planes for Linear Systems with Real Eigenvalues. Complex Eigenvalues. The Special Cases: Repeated and Zero Eigenvalues. Second-Order Linear Equations. The Trace-Determinant Plane. Linear Systems in Three Dimensions. Labs for Chapter 3.

4. FORCING AND RESONANCE.

Forced Harmonic Oscillators. Sinusoidal Forcing and Resonance. Undamped Forcing and Resonance. Quantitative Analysis of the Forced Harmonic Analysis. The Tacoma Narrows Bridge. Labs for Chapter 4.

5. NONLINEAR SYSTEMS.

Equilibrium Point Analysis. Qualitative Analysis. Hamiltonian Systems. Dissipative Systems. Nonlinear Systems in Three Dimensions. Labs for Chapter 5.

6. LAPLACE TRANSFORMS.

Laplace Transforms. Discontinuous Functions. Second-Order Equations. Delta Functions and Impulse Forcing. Convolutions. The Qualitative Theory of Laplace Transforms. Labs for Chapter 6.

7. NUMERICAL METHODS.

Numerical Error in Euler's Method. Improving Euler's Method. The Runge-Kutta Method. The Effects of Finite Arithmetic. Labs for Chapter 7.

8. DISCRETE DYNAMICAL SYSTEMS.

The Discrete Logistic Equation. Fixed and Periodic Points. Bifurcations. Chaos. Chaos in the Lorenz System. Labs for Chapter 8.

HINTS AND ANSWERS.

INDEX.