18210182TM

An introduction to ordinary differential equations
James C. Robinson
18210182

TABLE DES MATIÈRES

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?

14 décembre 2004