Elementary Differential Equations (8E) by Earl D. Rainville, Phillip E. Bedient, Richard E. Bedient
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About this book :-
Elementary Differential Equations (8E) written by
Earl D. Rainville, Phillip E. Bedient, Richard E. Bedient .
The new geometric material appears mainly in Sections 1.4 and 11.8. In the former we introduce students to the idea of a family of curves as solutions to a differential equation, and in the latter, the concept of the phase plane of a system of equations is presented. We have moved the treatment of systems of equations to an earlier place in the text.
Of all areas of mathematics covered in a typical undergraduate curriculum, the field of differential equations is arguably the most affected by the computer. Numerous packages have been produced which are either designed specifically for differential equations, or have subpackages designed for that material. We have made the rather arbitrary decision to present our computer examples using the Maple package. We could have equally well chosen any of the other Computer Algebra Systems such as Mathematica, Matlab, or Derive. Further, there are a number of numerical graphing packages that are more efficient for producing geometric results. Among the more commonly available are MacMath and Phaser.
Each computer supplement contains an example from the corresponding chapter, worked out with the aid of Maple. Subsequently a set of computer exercises is presented which can be solved using whichever package is available to the student. It is our hope that these brief introductions will encourage users to look beyond the text for further computer explorations.
(Earl D. Rainville)
Book Detail :-
Title: Elementary Differential Equations
Author(s): Earl D. Rainville, Phillip E. Bedient, Richard E. Bedient
Publisher: Prentice Hall
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About Author :-
The author Earl David Rainville (1907 – 1966) was the professor taught in the Department of Engineering Mathematics at the University of Michigan, where he began as an assistant professor in 1941. He studied at the University of Colorado, receiving his B.A. there in 1930 before going on to graduate studies at Michigan, where he received his Ph.D. in 1939 under the supervision of Ruel Churchill. He died on April 29, 1966.
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Book Contents :-
Elementary Differential Equations (8E) written by
Earl D. Rainville, Phillip E. Bedient, Richard E. Bedient
cover the following topics.
1. Definitions, Elimination of Arbitrary Constants
2. Equations of Order One
3. Elementary Applications
4. Additional Topics on Equations of Order One
5. Linear Differential Equations
6. Linear Equations with Constant Coefficients
7. Nonhomogeneous Equations: Undetermined Coefficients
8. Variation of Parameters
9. Inverse Differential Operators
11. The Laplace Transform
12. Inverse Transforms
13. Linear Systems of Equations
14. Electric Circuits and Networks
15. The Existence and Uniqueness of Solutions
16. Nonlinear Equations
17. Power Series Solutions
18. Solutions Near Regular Singular Points
19. Equations of Hypergeometric Type
20. Numerical Methods
21. Partial Differential Equations
22. Orthogonal Sets
23. Fourier Series
24. Boundary Value Problems
25. Additional Properties of the Laplace Transform
26. Partial Differential Equations; Transform Methods
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