An Introduction to Ordinary Differential Equations
This refreshing, introductory textbook covers both standard techniques for solving ordinary differential equations, as well as introducing students to qualitative methods such as phase-plane analysis. The presentation is concise, informal yet rigorous; it can be used either for 1-term or 1-semester courses. Topics such as Euler's method, difference equations, the dynamics of the logistic map, and the Lorenz equations, demonstrate the vitality of the subject, and provide pointers to further study. The author also encourages a graphical approach to the equations and their solutions, and to that end the book is profusely illustrated. The files to produce the figures using MATLAB are all provided in an accompanying website. Numerous worked examples provide motivation for and illustration of key ideas and show how to make the transition from theory to practice. Exercises are also provided to test and extend understanding: solutions for these are available for teachers.
1100943606
An Introduction to Ordinary Differential Equations
This refreshing, introductory textbook covers both standard techniques for solving ordinary differential equations, as well as introducing students to qualitative methods such as phase-plane analysis. The presentation is concise, informal yet rigorous; it can be used either for 1-term or 1-semester courses. Topics such as Euler's method, difference equations, the dynamics of the logistic map, and the Lorenz equations, demonstrate the vitality of the subject, and provide pointers to further study. The author also encourages a graphical approach to the equations and their solutions, and to that end the book is profusely illustrated. The files to produce the figures using MATLAB are all provided in an accompanying website. Numerous worked examples provide motivation for and illustration of key ideas and show how to make the transition from theory to practice. Exercises are also provided to test and extend understanding: solutions for these are available for teachers.
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An Introduction to Ordinary Differential Equations

An Introduction to Ordinary Differential Equations

by James C. Robinson
An Introduction to Ordinary Differential Equations
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An Introduction to Ordinary Differential Equations

An Introduction to Ordinary Differential Equations

by James C. Robinson

Overview

This refreshing, introductory textbook covers both standard techniques for solving ordinary differential equations, as well as introducing students to qualitative methods such as phase-plane analysis. The presentation is concise, informal yet rigorous; it can be used either for 1-term or 1-semester courses. Topics such as Euler's method, difference equations, the dynamics of the logistic map, and the Lorenz equations, demonstrate the vitality of the subject, and provide pointers to further study. The author also encourages a graphical approach to the equations and their solutions, and to that end the book is profusely illustrated. The files to produce the figures using MATLAB are all provided in an accompanying website. Numerous worked examples provide motivation for and illustration of key ideas and show how to make the transition from theory to practice. Exercises are also provided to test and extend understanding: solutions for these are available for teachers.

Product Details

ISBN-13: 9781139637046
Publisher: Cambridge University Press
Publication date: 01/08/2004
Sold by: Barnes & Noble
Format: eBook
File size: 14 MB
Note: This product may take a few minutes to download.

Table of Contents

Introduction; Part I. First Order Differential Equations: 1. Radioactive decay and carbon dating; 2. Integration variables; 3. Classification of differential equations; 4. Graphical representation of solutions using MATLAB; 5. 'Trivial' differential equations; 6. Existence and uniqueness of solutions; 7. Scalar autonomous ODEs; 8. Separable equations; 9. First order linear equations and the integrating factor; 10. Two 'tricks' for nonlinear equations; Part II. Second Order Linear Equations With Constant Coefficients: 11. Second order linear equations: general theory; 12. Homogeneous 2nd order linear ODEs; 13. Oscillations; 14. Inhomogeneous 2nd order linear equations; 15. Resonance; 16. Higher order linear equations; Part III. Linear Second Order Equations With Variable Coefficients: 17. Reduction of order; 18. The variation of constants formula; 19. Cauchy-Euler equations; 20. Series solutions of second order linear equations; Part IV. Numerical Methods and Difference Equations: 21. Euler's method; 22. Difference equations; 23. Nonlinear first order difference equations; 24. The logistic map; Part V. Coupled Linear Equations: 25. Vector first order equations and higher order equations; 26. Explicit solutions of coupled linear systems; 27. Eigenvalues and eigenvectors; 28. Distinct real eigenvalues; 29. Complex eigenvalues; 30. A repeated real eigenvalue; 31. Summary of phase portraits for linear equations; Part VI. Coupled Nonlinear Equations: 32. Coupled nonlinear equations; 33. Ecological models; 34. Newtonian dynamics; 35. The 'real' pendulum; 36. Periodic orbits; 37. The Lorenz equations; 38. What next?
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Related Subjects

Science & Technology
Mathematics
Mathematical Equations
Mathematical Equations - Differential
Science & Technology
Mathematics
Mathematical Equations
Mathematical Equations - Differential

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