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An Introduction to Ordinary Differential Equations

An Introduction to Ordinary Differential Equations

$89.99 (X)

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  • Date Published: February 2004
  • availability: Available
  • format: Paperback
  • isbn: 9780521533911

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  • 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. Matlab is used to generate graphical representations of solutions. Numerous exercises are featured and proved solutions are available for teachers.

    • Ideal for undergraduate mathematics students
    • Solutions to exercises available to lecturers from solutions@cambridge.org
    • Full of illustrations, worked examples, exercises and accompanying MATLAB code
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    Reviews & endorsements

    'The presentation is sensitive to the needs of students, with careful algebraic steps included in most cases. Appendices on basic required mathematical techniques are also included.' Mathematical Reviews

    'The book is recommended as a textbook for one-term or one-semester course.' Zentralblatt MATH

    '… will be useful to anybody wanting to teach or learn elements of ordinary differential equations in the beginnings of their mathematical studies.' European Mathematical Society Newsletter

    '… it is written in a friendly and informal style and covers a wide and interesting collection of topics.' Contemporary Physics

    'This is an excellent book which probably would have been most welcome to older students of differential equations had it existed and which will be of great value to those currently studying the subject.' The Mathematical Gazette

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    Product details

    • Date Published: February 2004
    • format: Paperback
    • isbn: 9780521533911
    • length: 414 pages
    • dimensions: 244 x 170 x 21 mm
    • weight: 0.83kg
    • contains: 147 b/w illus. 120 exercises
    • availability: Available
  • Table of Contents

    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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    An Introduction to Ordinary Differential Equations

    James C. Robinson

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  • Instructors have used or reviewed this title for the following courses

    • Ordinary Differential Equations
  • Author

    James C. Robinson, University of Warwick

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