Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review

by Granino A. Korn, Theresa M. Korn

Overview

Anyone whose work involves mathematics and its methodology — especially engineers and scientists — will appreciate this authoritative handbook, which provides convenient access to information from every area of mathematics. A reliable source of helpful definitions, theorems, and formulas, it features an easy-to-follow format outlining mathematical methods for speedy, accurate solutions to the most demanding problems.Among the topics covered are Fourier transforms, z transforms, linear and nonlinear programming, calculus of variations, random-process theory, special functions, combinatorial analysis, numerical methods, game theory, and much more. By concisely tabulating related formulas and omitting proofs, the authors have packed a remarkably large amount of material into a single, handy volume. Appropriate introductions, notes, and cross-references appear throughout the text, showing the interrelations of various topics and their significance to science and engineering.Illustrated throughout with numerous figures and tables, this volume represents a valuable resource for both students and professionals.

Product Details

ISBN-13:	9780486320236
Publisher:	Dover Publications
Publication date:	03/29/2013
Series:	Dover Civil and Mechanical Engineering
Sold by:	Barnes & Noble
Format:	eBook
Pages:	1152
File size:	155 MB
Note:	This product may take a few minutes to download.

Table of Contents

PrefaceChapter 1. Real and Complex Numbers. Elementary Algebra.1.1. Introduction. The Real-number System1.2. "Powers, Roots, Logarithms, and Factorials. Sum and Product Notation"1.3. Complex Numbers1.4. Miscellaneous Formulas1.5. Determinants1.6. Algebraic Equations: General Theorems1.7. Factoring of Polynomials and Quotients of Polynomials. Partial Fractions1.8. "Linear, Quadratic, Cubic, and Quartic Equations"1.9. Systems of Simultaneous Equations1.10. "Related Topics, References, and Bibliography"Chapter 2. Plane Analytic Geometry2.1. Introduction and Basic Concepts2.2. The Straight Line2.3. Relations Involving Points and Straight Lines2.4. Second-order Curves (Conic Sections)2.5. "Properties of Circles, Ellipses, Hyperbolas, and Parabolas"2.6. Higher Plane Curves2.7. "Related Topics, References, and Bibliography"Chapter 3. Solid Analytic Geometry3.1. Introduction and Basic Concepts3.2. The Plane3.3. The Straight Line3.4. "Relations Involving Points, Planes, and Straight Lines"3.5. Quadric Surfaces3.6. "Related Topics, References, and Bibliography"Chapter 4. Functions and Limits. Differential and Integral Calculus4.1. Introduction4.2. Functions4.3. "Point Sets, Intervals, and Regions"4.4. "Limits, Continuous Functions, and Related Topics"4.5. Differential Calculus4.6. Integrals and Integration4.7. Mean-value Theorems. Values of Indeterminate Forms. Weierstrass's Approximation Theorems.4.8. "Infinite Series, Infinite Products, and Continued Fractions"4.9. Tests for the Convergence and Uniform Convergence of Infinite Series and Improper Integrals4.10. Representation of Functions by Infinite Series and Integrals. Power Series and Taylor's Expansion4.11. Fourier Series and Fourier Integrals4.12. "Related Topics, References, and Bibliography"Chapter 5. Vector Analysis5.1. Introduction5.2. Vector Algebra5.3. Vector Calculus: Functions of Scalar Parameter5.4. Scalar and Vector Fields5.5. Differential Operators5.6. Integral Theorems5.7. Specification of a Vector Field in Terms of Its Curl and Divergence5.8. "Related Topics, References, and Bibliography"Chapter 6. Curvilinear Coordinate Systems6.1. Introduction6.2. Curvilinear Coordinate Systems6.3. Representation of Vectors in Terms of Components6.4. Orthogonal Coordinate Systems. Vector Relations in Terms of Orthogonal Components6.5. Formulas Relating to Special Orthogonal Coordinate Systems6.6. "Related Topics, References, and Bibliography"Chapter 7. Functions of a Complex Variable7.1. Introduction7.2. Functions of a Complex Variable. Regions of the Complex-number Plane7.3. "Analytic (Regular, Holomorphic) Functions"7.4. Treatment of Multiple-valued Functions7.5. Integral Theorems and Series Expansions7.6. Zeros and Isolated Singularities7.7. Residues and Contour Integration7.8. Analytic Continuation7.9. Conformal Mapping7.10. Functions Mapping Specified Regions onto the Unit Circle7.11. "Related Topics, References, and Bibliography"Chapter 8. The Laplace Transformation and Other Functional Transformations8.1. Introduction8.2. The Laplace Transformation8.3. Correspondence between Operations on Object and Result Functions8.4. Table of Laplace-transform Pairs and Computation of Inverse Laplace Transforms8.5. "Formal" Laplace Transformation of Impulse-function Terms"8.6. Some Other Integral Transformations8.7. "Finite Integral Transforms, Generating Functions, and z Transforms"8.8. "Related Topics, References, and Bibliography"Chapter 9. Ordinary Differential Equations9.1. Introduction9.2. First-order Equations9.3. Linear Differential Equations9.4. Linear Differential Equations with Constant Coefficients9.5. Nonlinear Second-order Equations9.6. Pfaffian Differential Equations9.7. "Related Topics, References, and Bibliography"Chapter 10. Partial Differential Equations10.1. Introduction and Survey10.2. Partial Differential Equations of the First Order10.3. "Hyperbolic, Parabolic, and Elliptic Partial Differential Equations. Characteristics."10.4.