Brian Kolo PhD Calculus

ISBN 13: 9781615800186

Calculus

 
9781615800186: Calculus
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Differential and integral calculus is widely used in scientific and engineering applications. This treatise introduces the fundamental principles of calculus typically encountered in applied mathematics. Integral calculus is examined in detail starting with a basic integral definition applicable to continuous nonnegative functions. This definition is extended to continuous functions that may be positive or negative. These definitions motivate the more general Riemann integral which is further generalized in the Riemann-Stieltjes integral. These integral definitions are then compared with the Lebesgue and Lebesgue-Stieltjes integral definitions. Differential and integral calculus is applied to graphing functions and computing arc length. These techniques are expanded to more advanced concepts such as repeated derivatives, repeated integrals, and calculus of variations. Differential calculus is used to formulate series expansions for analytic functions. McLaren, Taylor, and Laurent series are each introduced. In addition, inversion series are introduced to solve problems of inverting power series. Finally, these techniques are used to compute infinite summations using generating functions. Both differential and integral calculus prove useful in transforming generating functions in various ways to compute these sums.

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Brian Kolo PhD
Published by Weatherford Press (2011)
ISBN 10: 1615800182 ISBN 13: 9781615800186
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