Umfang:
xix, 716 Seiten
,
Diagramme
,
454 grams
Ausgabe:
Fourth edition
ISBN:
9780367252571
,
9781032118932
Serie:
Advances in applied mathematics
Inhalt:
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 applicableThe idea behind the methodThe procedure for carrying out the methodAt least one simple example of the methodAny cautions that should be exercisedNotes for more advanced usersThe fourth edition includes corrections, many supplied by readers, as well as many new methods and techniques.
Inhalt:
MATLAB Programming Language. 230. Octave Programming Language. 231. Python Programming Language. 232. R Programming Language. 233. Sage Computer Algebra System. BiographiesDaniel Zwillinger has more than 35 years of proven technical expertise in numerous areas of engineering and the physical sciences. He earned a Ph.D. in applied mathematics from the California Institute of Technology. He is the Editor of CRC Standard Mathematical Tables and Formulas, 33rd edition and also Table of Integrals, Series, and Products, Gradshteyn and Ryzhik. He serves as the Series Editor on the CRC Series of Advances in Applied Mathematics.Vladimir A. Dobrushkin is a Professor at the Division of Applied Mathematics, Brown University. He holds a Ph.D. in Applied mathematics and Dr.Sc. in mechanical engineering.
Inhalt:
He is the author of three books for CRC Press, including Applied Differential Equations: The Primary Course, Applied Differential Equations with Boundary Value Problems, and Methods in Algorithmic Analysis
Anmerkung:
These new and corrected entries make necessary improvements in this edition. Table of ContentsI.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.
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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.
Weitere Ausg.:
Erscheint auch als Online-Ausgabe ISBN 978-0-429-28683-4
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Differentialgleichung
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