An Introduction to Ordinary Differential Equations

ISBN-13: 9780521533911 / Angielski / Miękka / 2004 / 414 str.

James C Robinson

Opis

This introduction to ordinary differential and difference equations is suited not only for mathematicians but for scientists and engineers as well. Exact solutions methods and qualitative approaches are covered, and many illustrative examples are included. Matlab is used to generate graphical representations of solutions. Numerous exercises are featured and proved solutions are available for teachers.

Recenzje

'This is an excellent book which probably would have been most welcome to older students of differential equations had it existed and which will be of great value to those currently studying the subject.' The Mathematical Gazette

Spis treści

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?