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The Second Edition provides substantial new coverage of the material, including three new chapters and a large appendix that contains solutions to almost all of the exercises in the book. Applications of some of these methods in statistics are discusses. Mathematics is vigorously and brilliantly pursued in our time on a very broad front; yet the authors of this text feel that not enough mathematical talent is devoted to furthering the interaction of mathematics with other sciences and disciplines.
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The symbiotic relationship between science and mathematics is shown by deriving and discussing several conservation laws, and vector calculus is utilized to describe a number of physical theories via partial differential equations. Students will learn that mathematics is the language that enables scientific ideas to be precisely formulated and that science is a source for the development of mathematics. Combining mathematical theory, physical principles, and engineering problems, Generalized Calculus with Applications to Matter and Forces examines generalized functions, including the Heaviside unit jump and the Dirac unit impulse and its derivatives of all orders, in one and several dimensions.
The text introduces the two main approaches to generalized functions: 1 as a nonuniform limit of a family of ordinary functions, and 2 as a functional over a set of test functions from which properties are inherited. The second approach is developed more extensively to encompass multidimensional generalized functions whose arguments are ordinary functions of several variables.
Featuring step-by-step examples with interpretations of results and discussions of assumptions and their consequences, Generalized Calculus with Applications to Matter and Forces enables readers to construct mathematical—physical models suited to new observations or novel engineering devices. Presents a treatment of stochastic calculus. This title gives its main applications in finance, biology and engineering. It presents the theory of stochastic calculus and its applications to an audience which possesses only a basic knowledge of calculus and probability.
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Generalized Calculus with Applications to Matter and Forces. Introduction to Stochastic Calculus with Applications.
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