An Introduction to Ordinary Differential Equations – James C. Robinson – 1st Edition


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.

This refreshing, introductory textbook covers both standard techniques for solving ordinary differential equations, as well as introducing students to qualitative methods such as phase-plane analysis. The presentation is concise, informal yet rigorous; it can be used either for 1-term or 1-semester courses.

Topics such as Euler’s method, difference equations, the dynamics of the logistic map, and the Lorenz equations, demonstrate the vitality of the subject, and provide pointers to further study. The author also encourages a graphical approach to the equations and their solutions, and to that end the book is profusely illustrated.

Matlab is used to generate graphical representations of solutions. The files to produce the figures using MATLAB are all provided in an accompanying file. Numerous worked examples provide motivation for and illustration of key ideas and show how to make the transition from theory to practice.

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  • 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?

  • Citation
    • Full Title: An Introduction to Ordinary Differential Equations
    • Author/s:
    • ISBN-10: 0521533910
    • ISBN-13: 9780521533911
    • Edition: 1st Edition
    • Topic: Math
    • Subtopic: Differential Equations
    • File Type: eBook
    • Idioma: English

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