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Advanced Calculus: Laplace Transforms

by Edward Walsh

468 pages; quality trade paperback (softcover); catalogue #05-3039; ISBN 1-4120-8041-X; US$28.95, C$33.29, EUR23.78, £16.65

The Laplace Transform is used to solve initial value problems involving differential equations. All steps included. Conventional methods are also discussed.

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About the Book

The book starts with the definition of the Laplace Transform and uses it to derive the Laplace Transforms of the elementary functions including; constant functions, polynomial functions, exponential functions, trigonometric functions, and hyperbolic functions. All steps in the derivations of the Laplace Transforms for these functions are included.

The concept of the Inverse Laplace Transform is then logically developed from the concept of the Laplace Transform. Numerous examples are provided for finding the Laplace Transforms of the various types of elementary functions and finding their corresponding Inverse Laplace Transforms.

The Product Rule is derived with all steps included. Also, the Laplace Transform of a derivative is derived with all steps included.

Finally, the following types of differential equations and their initial value problems are solved using both conventional methods and the Laplace Transform method:

•First-order homogenous linear differential equations with constant coefficients
•First-order non-homogenous linear differential equations with constant coefficients
•Second-order homogenous linear differential equations with constant coefficients
•Second-order non-homogenous linear differential equations with constant coefficients

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About the Author

Edward Walsh graduated with a B.A. degree in Mathematics from Moorhead State College in Moorhead, Minnesota where he took a year of applied mathematics, including courses in Fourier Series and Transforms; Partial Differential Equations and Boundary Value Problems; and Complex Analysis.

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Excerpts

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Catalogue Information

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