| Description |
1 online resource |
| Contents |
Intro; Preface; Contents; 1 Complex Functions; 1.1 Complex Functions of Real Variable; 1.2 Complex Functions of Complex Variable; 1.3 Elementary Complex Functions; 1.4 Complex Integrals; 1.5 Complex Series; 2 Special Functions; 2.1 Euler's Functions; 2.2 Bessel's Functions; 2.3 Orthogonal Polynomials; 2.4 Legendre's Polynomials; 2.5 Chebyshev's Polynomials; 2.6 Hermite's Polynomials; 2.7 Laguerre's Polynomials; 3 Operational Calculus; 3.1 Laplace's Transform; 3.2 Operational Methods; 3.3 Applications; 3.4 Differential Equations with Constant Coefficients |
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3.5 Differential Equations with Variable Coefficients3.6 Integral Equations; 3.7 Partial Differential Equations; 3.8 Some Improper Integrals; 4 Fourier's Transform; 4.1 Fourier Series; 4.2 Fourier's Single Integral Formula; 4.3 Fourier's Transform in L1; 4.4 Fourier's Transform in L2; 5 Calculus of Variations; 5.1 Introduction; 5.2 Euler's Equation; 5.3 Generalizations of Euler's Equation; 5.4 Sufficent Conditions for Extremum; 5.5 Isoperimetric Problems; 5.6 Moving Boundary Problems; 6 Quasi-linear Equations; 6.1 Canonical Form for n=2; 6.2 Canonical Form for n>2; 7 Hyperbolical Equations |
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7.1 Problem of the Infinite Vibrating Chord7.2 Initial-Boundary Values Problems; 7.3 Cauchy's Problem; 7.4 Problem of the Finite Vibrating Chord; 8 Parabolical Equations; 8.1 The Finite Problem of Heat; 8.2 Initial-Boundary Value Problems; 8.3 Method of the Green's Function; 8.4 Cauchy's Problem; 9 Elliptic Partial Differential Equations; 9.1 Introductory Formulas; 9.2 Potentials; 9.3 Boundary Values Problems; 10 Optimal Control; 10.1 Preparatory Notions; 10.2 Problems of Optimal Control; 10.3 Linear Problems of Control; 10.4 Problems of Quadratic Control |
| Summary |
This book highlights the remarkable importance of special functions, operational calculus, and variational methods. A considerable portion of the book is dedicated to second-order partial differential equations, as they offer mathematical models of various phenomena in physics and engineering. The book provides students and researchers with essential help on key mathematical topics, which are applied to a range of practical problems. These topics were chosen because, after teaching university courses for many years, the authors have found them to be essential, especially in the contexts of technology, engineering and economics. Given the diversity topics included in the book, the presentation of each is limited to the basic notions and results of the respective mathematical domain. Chapter 1 is devoted to complex functions. Here, much emphasis is placed on the theory of holomorphic functions, which facilitate the understanding of the role that the theory of functions of a complex variable plays in mathematical physics, especially in the modeling of plane problems. In addition, the book demonstrates the importance of the theories of special functions, operational calculus, and variational calculus. In the last chapter, the authors discuss the basic elements of one of the most modern areas of mathematics, namely the theory of optimal control |
| Bibliography |
Includes bibliographical references |
| Notes |
Online resource; title from PDF title page (EBSCO, viewed February 19, 2018) |
| Subject |
Functions of several real variables.
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Functions, Special.
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Calculus, Operational.
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Calculus of variations.
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Mathematical modelling.
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Maths for engineers.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Calculus, Operational
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Functions of several real variables
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Functions, Special
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| Form |
Electronic book
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| Author |
Öchsner, Andreas, author.
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| ISBN |
9783319746845 |
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3319746847 |
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