Handbook of Differential Equations (4) (Advances in Applied Mathematics)

Synopsis

Through the previous three editions, Handbook of Differential Equations has proven an invaluable reference for anyone working within the field of mathematics, including academics, students, scientists, and professional engineers. The book is a compilation of methods for solving and approximating differential equations. These include the most widely applicable methods for solving and approximating differential equations,　as well as　numerous methods. Topics include methods for ordinary differential equations, partial differential equations, stochastic differential equations, and systems of such equations. Included for nearly every method are: The types of equations to which the method is applicable The idea behind the method The procedure for carrying out the method At least one simple example of the method Any cautions that should be exercised Notes for more advanced users The fourth edition includes corrections, many supplied by readers, as well as many new methods and techniques. These new and corrected entries make necessary improvements in this edition. Table of Contents I.A Definitions and Concepts. 1. Definition of Terms. 2. Alternative Theorems. 3. Bifurcation Theory. 4. Chaos in Dynamical Systems. 5. Classification of Partial Differential Equations. 6. Compatible Systems. 7. Conservation Laws. 8. Differential Equations – Diagrams. 9. Differential Equations – Symbols. 10. Differential Resultants. 11. Existence and Uniqueness Theorems. 12. Fixed Point Existence Theorems. 13. Hamilton – Jacobi Theory. 14. Infinite Order Differential Equations. 15. Integrability of Systems. 16. Inverse Problems. 17. Limit Cycles. 18. PDEs & Natural Boundary Conditions. 19. Normal Forms: Near-Identity Transformations. 20. q-Differential Equations. 21. Quaternionic Differential Equations. 22. Self-Adjoint Eigenfunction Problems. 23. Stability Theorems. 24. Stochastic Differential Equations. 25. Sturm–Liouville Theory. 26. Variational Equations. 27. Web Resources. 28. Well-Posed Differential Equations. 29. Wronskians & Fundamental Solutions. 30. Zeros of Solutions. I.B. Transformations. 31. Canonical Forms. 32. Canonical Transformations. 33. Darboux Transformation. 34. An Involutory Transformation. 35. Liouville Transformation – 1. 36. Liouville Transformation – 2. 37. Changing Linear ODEs to a First Order System. 38. Transformations of Second Order Linear ODEs – 1. 39. Transformations of Second Order Linear ODEs – 2. 40. Transforming an ODE to an Integral Equation. 41. Miscellaneous ODE Transformations. 42. Transforming PDEs Generically. 43. Transformations of PDEs. 44. Transforming a PDE to a First Order System. 45. Prüfer Transformation. 46. Modified Prüfer Transformation. II. Exact Analytical Methods. 47. Introduction to Exact Analytical Methods. 48. Look-Up Technique. 49. Look-Up ODE Forms. II.A Exact Methods for ODEs. 50. Use of the Adjoint Equation. 51. An Nth Order Equation. 52. Autonomous Equations – Independent Variable Missing. 53. Bernoulli Equation. 54. Clairaut's Equation. 55. Constant Coefficient Linear ODEs. 56 Contact Transformation. 57. Delay Equations. 58. Dependent Variable Missing. 59. Differentiation Method. 60. Differential Equations with Discontinuities. 61. Eigenfunction Expansions. 62. Equidimensional-in-x Equations. 63. Equidimensional-in-y Equations. 64. Euler Equations. 65. Exact First Order Equations. 66. Exact Second Order Equations. 67. Exact Nth Order Equations. 68. Factoring Equations. 69. Factoring/Composing Operators. 70. Factorization Method. 71. Fokker–Planck Equation. 72. Fractional Differential Equations. 73. Free Boundary Problems. 74. Generating Functions. 75. Green's Functions. 76. ODEs with Homogeneous Functions. 77. Hypergeometric Equation. 78. Method of Images. 79. Integrable Combinations. 80. Integ

Copyright:

2022

Book Details

Book Quality:

Publisher Quality

Book Size:

716 Pages

ISBN-13:

9781000468182

Related ISBNs:

9780429286834, 9781032118932, 9780367252571

Publisher:

CRC Press

Date of Addition:

08/28/23

Copyrighted By:

Taylor & Francis Group, LLC

Adult content:

No

Language:

English

Has Image Descriptions:

No

Categories:

Nonfiction, Mathematics and Statistics

Submitted By:

Bookshare Staff

Usage Restrictions:

This is a copyrighted book.