James C. Robinson (University of Warwick)

An Introduction to Ordinary Differential Equations

• Broschiertes Buch

Produktbeschreibung

A first introduction to ordinary differential and difference equations, accessible for mathematicians, scientists and engineers. All important and relevant approaches are covered, and many illustrative examples are included. MATLAB is used to generate graphical representations of solutions, for which code is supplied. Exercises and worked solutions are available for teachers.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 414
• Erscheinungstermin: 15. Dezember 2014
• Englisch
• Abmessung: 244mm x 170mm x 23mm
• Gewicht: 730g
• ISBN-13: 9780521533911
• ISBN-10: 0521533910
• Artikelnr.: 21673337

Inhaltsangabe

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?