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.
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.
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?
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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