Generalized Calculus With Applications To Matter And Forces
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Generalized Calculus with Applications to Matter and Forces
Author | : Luis Manuel Braga de Costa Campos |
Publsiher | : CRC Press |
Total Pages | : 885 |
Release | : 2014-04-18 |
Genre | : Mathematics |
ISBN | : 9781482281576 |
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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 genera
Generalized Calculus with Applications to Matter and Forces
Author | : Luis Manuel Braga de Costa Campos |
Publsiher | : CRC Press |
Total Pages | : 888 |
Release | : 2014-04-18 |
Genre | : Mathematics |
ISBN | : 9781420071153 |
Download Generalized Calculus with Applications to Matter and Forces Book in PDF, Epub and Kindle
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. As part of a series of books for engineers and scientists exploring advanced mathematics, Generalized Calculus with Applications to Matter and Forces presents generalized functions from an applied point of view, tackling problem classes such as: Gauss and Stokes’ theorems in the differential geometry, tensor calculus, and theory of potential fields Self-adjoint and non-self-adjoint problems for linear differential equations and nonlinear problems with large deformations Multipolar expansions and Green’s functions for elastic strings and bars, potential and rotational flow, electro- and magnetostatics, and more This third volume in the series Mathematics and Physics for Science and Technology is designed to complete the theory of functions and its application to potential fields, relating generalized functions to broader follow-on topics like differential equations. 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.
Linear Differential Equations and Oscillators
Author | : Luis Manuel Braga da Costa Campos |
Publsiher | : CRC Press |
Total Pages | : 228 |
Release | : 2019-11-05 |
Genre | : Mathematics |
ISBN | : 9780429639623 |
Download Linear Differential Equations and Oscillators Book in PDF, Epub and Kindle
Linear Differential Equations and Oscillators is the first book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This first book consists of chapters 1 and 2 of the fourth volume. The first chapter covers linear differential equations of any order whose unforced solution can be obtained from the roots of a characteristic polynomial, namely those: (i) with constant coefficients; (ii) with homogeneous power coefficients with the exponent equal to the order of derivation. The method of characteristic polynomials is also applied to (iii) linear finite difference equations of any order with constant coefficients. The unforced and forced solutions of (i,ii,iii) are examples of some general properties of ordinary differential equations. The second chapter applies the theory of the first chapter to linear second-order oscillators with one degree-of-freedom, such as the mechanical mass-damper-spring-force system and the electrical self-resistor-capacitor-battery circuit. In both cases are treated free undamped, damped, and amplified oscillations; also forced oscillations including beats, resonance, discrete and continuous spectra, and impulsive inputs. Describes general properties of differential and finite difference equations, with focus on linear equations and constant and some power coefficients Presents particular and general solutions for all cases of differential and finite difference equations Provides complete solutions for many cases of forcing including resonant cases Discusses applications to linear second-order mechanical and electrical oscillators with damping Provides solutions with forcing including resonance using the characteristic polynomial, Green' s functions, trigonometrical series, Fourier integrals and Laplace transforms
Generalized Functions
Author | : Ram P. Kanwal |
Publsiher | : Springer Science & Business Media |
Total Pages | : 502 |
Release | : 2004-07-23 |
Genre | : Mathematics |
ISBN | : 0817643435 |
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Provides a more cohesive and sharply focused treatment of fundamental concepts and theoretical background material, with particular attention given to better delineating connections to varying applications Exposition driven by additional examples and exercises
Notes on the Principles of Pure and Applied Calculation
Author | : James Challis |
Publsiher | : Unknown |
Total Pages | : 808 |
Release | : 1869 |
Genre | : Mathematical physics |
ISBN | : UOM:39015067305527 |
Download Notes on the Principles of Pure and Applied Calculation Book in PDF, Epub and Kindle
Generalized Fractional Order Differential Equations Arising in Physical Models
Author | : Santanu Saha Ray,Subhadarshan Sahoo |
Publsiher | : CRC Press |
Total Pages | : 351 |
Release | : 2018-11-13 |
Genre | : Mathematics |
ISBN | : 9780429771798 |
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This book analyzes the various semi-analytical and analytical methods for finding approximate and exact solutions of fractional order partial differential equations. It explores approximate and exact solutions obtained by various analytical methods for fractional order partial differential equations arising in physical models.
General Catalog
Author | : University of Colorado (Boulder campus) |
Publsiher | : Unknown |
Total Pages | : 432 |
Release | : 1954 |
Genre | : Universities and colleges |
ISBN | : WISC:89093678183 |
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A Treatise on Universal Algebra
Author | : Alfred North Whitehead |
Publsiher | : Unknown |
Total Pages | : 628 |
Release | : 1898 |
Genre | : Algebra |
ISBN | : UOM:39015017395149 |
Download A Treatise on Universal Algebra Book in PDF, Epub and Kindle