Integrals Related to the Error Function
Integrals Related to the Error Function

Author: Nikolai E. Korotkov

Publisher: CRC Press

Published: 2020-03-05

Total Pages: 57

ISBN-13: 1000033090

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Integrals Related to the Error Function presents a table of integrals related to the error function, including indefinite and improper definite integrals. Most of the formulas in this book have not been presented in other tables of integrals or have been presented only for some special cases of parameters or for integration only along the real axis of the complex plane. Many of the integrals presented here cannot be obtained using a computer (except via an approximate numerical integration). Additionally, for improper integrals, this book emphasizes the necessary and sufficient conditions for the validity of the presented formulas, including trajectory for going to infinity on the complex plane; such conditions are usually not given in computer-assisted analytical integration and often not presented in the previously published tables of integrals. Features The first book in English language to present a comprehensive collection of integrals related to the error function Useful for researchers whose work involves the error function (e.g., via probability integrals in communication theory). Additionally, it can also be used by broader audience.

Handbook of Mathematical Functions
Handbook of Mathematical Functions

Author: Milton Abramowitz

Publisher: Courier Corporation

Published: 1965-01-01

Total Pages: 1068

ISBN-13: 9780486612720

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An extensive summary of mathematical functions that occur in physical and engineering problems

Active Calculus 2018
Active Calculus 2018

Author: Matthew Boelkins

Publisher: Createspace Independent Publishing Platform

Published: 2018-08-13

Total Pages: 560

ISBN-13: 9781724458322

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Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Each section of Active Calculus has at least 4 in-class activities to engage students in active learning. Normally, each section has a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on the goals and structure of the text can be found in the preface.

Programming for Computations - Python
Programming for Computations - Python

Author: Svein Linge

Publisher: Springer

Published: 2016-07-25

Total Pages: 244

ISBN-13: 3319324284

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This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

Programming for Computations - MATLAB/Octave
Programming for Computations - MATLAB/Octave

Author: Svein Linge

Publisher: Springer

Published: 2016-08-01

Total Pages: 228

ISBN-13: 3319324527

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This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

Table of Integrals, Series, and Products
Table of Integrals, Series, and Products

Author: I. S. Gradshteyn

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 1207

ISBN-13: 1483265641

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Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.

Asymptotic Methods For Integrals
Asymptotic Methods For Integrals

Author: Nico M Temme

Publisher: World Scientific

Published: 2014-10-31

Total Pages: 628

ISBN-13: 9814612170

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This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals.The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on.

Special Functions in Physics with MATLAB
Special Functions in Physics with MATLAB

Author: Wolfgang Schweizer

Publisher: Springer Nature

Published: 2021-03-25

Total Pages: 282

ISBN-13: 3030642321

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This handbook focuses on special functions in physics in the real and complex domain. It covers more than 170 different functions with additional numerical hints for efficient computation, which are useful to anyone who needs to program with other programming languages as well. The book comes with MATLAB-based programs for each of these functions and a detailed html-based documentation. Some of the explained functions are: Gamma and Beta functions; Legendre functions, which are linked to quantum mechanics and electrodynamics; Bessel functions; hypergeometric functions, which play an important role in mathematical physics; orthogonal polynomials, which are largely used in computational physics; and Riemann zeta functions, which play an important role, e.g., in quantum chaos or string theory. The book’s primary audience are scientists, professionals working in research areas of industries, and advanced students in physics, applied mathematics, and engineering.

Handbook of Mathematical Formulas and Integrals
Handbook of Mathematical Formulas and Integrals

Author: Alan Jeffrey

Publisher:

Published: 2000

Total Pages: 472

ISBN-13:

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If there is a formula to solve a given problem in mathematics, it can be found in Alan Jeffrey's Handbook of Mathematical Formulas and Integrals. Thanks to its unique thumb-tab indexing feature, answers are easy to find based upon the type of problem they solve. The handbook covers important formulas, functions, relations, and methods from algebra, trigonomic and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, both ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Equations are computer-validated with Scientific WorkPlace and Mathematica. -- Back cover