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Cover: 9780521533911 | An Introduction to Ordinary Differential Equations | James C. Robinson
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An Introduction to Ordinary Differential Equations
Taschenbuch von James C. Robinson
Sprache: Englisch

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Beschreibung
A first introduction to ordinary differential and difference equations. The presentation is very accessible, making the book suited not only for mathematicians, but also for scientists and engineers, for whom the subject is essential. Both exact solution methods and qualitative approaches are covered, and many illustrative examples are included. MATLAB is used to generate graphical representations of solutions: code is supplied for this. Exercises are plentiful and worked solutions are available for teachers.
A first introduction to ordinary differential and difference equations. The presentation is very accessible, making the book suited not only for mathematicians, but also for scientists and engineers, for whom the subject is essential. Both exact solution methods and qualitative approaches are covered, and many illustrative examples are included. MATLAB is used to generate graphical representations of solutions: code is supplied for this. Exercises are plentiful and worked solutions are available for teachers.
Inhaltsverzeichnis
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?
Details
Erscheinungsjahr: 2014
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 414
Inhalt: Kartoniert / Broschiert
ISBN-13: 9780521533911
ISBN-10: 0521533910
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Robinson, James C.
Hersteller: Cambridge University Press
Maße: 244 x 170 x 23 mm
Von/Mit: James C. Robinson
Erscheinungsdatum: 15.12.2014
Gewicht: 0,711 kg
preigu-id: 102528249
Inhaltsverzeichnis
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?
Details
Erscheinungsjahr: 2014
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 414
Inhalt: Kartoniert / Broschiert
ISBN-13: 9780521533911
ISBN-10: 0521533910
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Robinson, James C.
Hersteller: Cambridge University Press
Maße: 244 x 170 x 23 mm
Von/Mit: James C. Robinson
Erscheinungsdatum: 15.12.2014
Gewicht: 0,711 kg
preigu-id: 102528249
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