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Schaum's Outline of Advanced Math for Engineers and Scientists (Schaum's Outlines)
出版社 :
Schaum Pub Co
出版年月 : 2009/09
Binding : Paperback
ISBN : 9780071635400
BookWeb価格 : THB 756.00 会員価格 : THB 680.00 在庫情報 : フルフィルメント・センターに在庫があります。 通常、3日以内に発送いたします。 言語 : English 
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内容情報
Source： ENG
Place of Publication： United States
Edition： Reprint
Subject Development： Study and Teaching
Academic Level： Undergraduate
Place of Publication： United States
Edition： Reprint
Subject Development： Study and Teaching
Academic Level： Undergraduate
Table of Contents
Review of Fundamental Concepts 1 (37) Real numbers Rules of algebra Functions Special types of functions Limits Continuity Derivatives Differentiation formulas Integrals Integration formulas Sequences and series Uniform convergence Taylor series Functions of two or more variables Partial derviatives Taylor series for functions of two or more variables Linear equations and determinants Maxima and minima Method of Lagrange multipliers Leibnitz's rule for differentiating an integral Multiple integrals Complex numbers Ordinary Differential Equations 38 (33) Definition of a differential equation Order of a differential equation Arbitrary contants Solution of a differential equation Differential equation of a family of curves Special first order equations and solutions Equations of higher order Existence and uniqueness of solutions Applications of differential equations Some special applications Mechanics Electric circuits Orthogonal trajectories Deflection of beams Miscellaneous problems Numerical methods for solving differential equations Linear Differential Equations 71 (27) General linear differential equation of order n. Existence and uniqueness theorem Operator notation Linear operators Fundamental theorem on linear differential equations Linear dependence and Wronskians Solutions of linear equations with constant coefficients Nonoperator techniques The complementary or homogeneous solution The particular solution Method of undetermined coefficients Method of variation of parameters Operator techniques Method of reduction of order Method of inverse operators Linear equations with variable coefficients Simultaneous differential equations Applications Laplace Transforms 98 (23) Definition of a Laplace transform Laplace transforms of some elementary functions Sufficient conditions for existence of Laplace transforms Inverse Laplace transforms Laplace transforms of derivatives The unit step function Some special theorems on Laplace transforms Partial fractions Solutions of differential equations by Laplace transforms Applications to physical problems Laplace inversion formulas Vector Analysis 121(26) Vectors and scalars Vector algebra Laws of vector algebra Unit vectors Rectangular unit vectors Components of a vector Dot or scalar product Cross or vector product Triple products Vector functions Limits, continuity and derivative of vector functions Geometric interpretation of a vector derivative Gradient, divergence and curl Formulas involving Δ Orthogonal curvilinear coordinates Jacobians Gradient, divergence, curl and Laplacian in orthogonal curvilinear Special curvilinear coordinates Multiple, Line and Surface Integrals and 147(35) Integral Theorems Double integrals Iterated integrals Triple integrals Transformations of multiple integrals Line integrals Vector notation for line integrals Evaluation of line integrals Properties of line integrals Simple closed curves Simply and multiplyconnected regions Green's theorem in the plane Conditions for a line integral to be independent of the path Surface integrals The divergence theorem Stokes' theorem Fourier Series 182(19) Periodic functions Fourier series Dirichlet conditions Odd and even functions Half range Fourier sine or cosine series Parseval's identity Differentiation and integration of Fourier series Complex notation for Fourier series Complex notation for Fourier series Orthogonal functions Fourier Integrals 201(9) The Fourier integral Equivalent forms of Fourier's integral theorem Fourier transforms Parseval's identities for Fourier integrals The convolution theorem Gamma, Beta and Other Special Functions 210(14) The gamma function Table of values and graph of the gamma function Asymptotic formula for Γ(n) Miscellaneous results involving the gamma function The beta function Dirichlet integrals Other special functions Error function Exponential integral Sine integral Cosine integral Fresnel sine integral Fresnel cosine integral Asymptotic series or expansions Bessel Functions 224(18) Bessel's differential equation Bessel functions of the first kind Bessel functions of the second kind Generating functions for Jn(x) Recurrence formulas Functions related to Bessel functions Hankel functions of first and second kinds Modified Bessel functions Ber, bei, ker, kei functions Equations transformed into Bessel's equation Asymptotic formulas for Bessel functions Zeros of Bessel functions Orthogonality of Bessel functions Series of Bessel functions Legendre Functions and Other Orthogonal 242(16) Functions Legendre's differential equation Legendre polynomials Generating function for Legendre polynomials Recurrence formulas Legendre functions of the second kind Orthogonality of Legendre polynomials Series of Legendre polynomials Associated Legendre functions Other special functions Hermite polynomials Laguerre polynomials SturmLioville systems Partial Differential Equations 258(28) Some definitions involving partial differential equations Linear partial differential equations Some important partial differential equations Heat conduction equation Vibrating string equation Laplace's equation Longitudinal vibrations of a beam Transverse vibrations of a beam Methods of solving boundaryvalue problems General solutions Separation of variables Laplace transform methods Complex Variables and Conformal Mapping 286(38) Functions Limits and continuity Derivatives CauchyRiemann equations Integrals Cauchy's theorem Cauchy's integral formulas Taylor's series Singular points Poles Laurent's series Residues Residue theorem Evaluation of definite integrals Conformal mapping Riemann's mapping theorem Some general transformations Mapping of a half plane on to a circle The SchwarzChristoffel transformation Solutions of Laplace's equation by conformal mapping Complex Inversion Formula for Laplace 324(18) Transforms The complex inversion formula The Bromwich contour Use of residue theorem in finding inverse Laplace transforms A sufficient condition for the integral around Γ to approach zero Modification of Bromwich contour in case of branch points Case of infinitely many singularities Applications to boundaryvalue problems Matrices 342(33) Definition of a matrix Some special definitions and operations involving matrices Determinants Theorems on determinants Inverse of a matrix Orthogonal and unitary matrices Orthogonal vectors Systems of linear equations Systems of n equations in n unknowns Cramer's rule Eigenvalues and eigenvectors Theorems on eigenvalues and eigenvectors Calculus of Variations 375(24) Maximum or minimum of an integral Euler's equation Constraints The variational notation Generalizations Hamilton's principle Lagrange's equations SturmLiouville systems and RayleighRitz methods Operator interpretation of matrices Index 399
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著者名 Ayres, Frank, Jr., Ph.D./ Mendelson, Elliott, Ph.D.
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