05699nam 22007573u 450 991100698770332120250609213943.01-5231-0674-30-486-79499-7(CKB)3710000000335099(EBL)1920034(SSID)ssj0001293105(PQKBManifestationID)12498948(PQKBTitleCode)TC0001293105(PQKBWorkID)11311522(PQKB)10500975(MiAaPQ)EBC1920034(Au-PeEL)EBL1920034(OCoLC)900346415(EXLCZ)99371000000033509920150119d2014|||| u|| |engur|n|---|||||txtccrApplied Mathematics for Engineers and Physicists Third Edition3rd ed.Newburyport Dover Publications20141 online resource (1760 p.)Dover Books on MathematicsDescription based upon print version of record.0-486-77951-3 Cover; Title Page; Copyright Page; Preface to The Dover Edition; Preface; Contents; Chapter 1 The Theory of Complex Variables; 1 Introduction; 2 Functions of a Complex Variable; 3 The Derivative and the Cauchy-Riemann Differential Equations; 4 Line Integrals of Complex Functions; 5 Cauchy's Integral Theorem; 6 Cauchy's Integral Formula; 7 Taylor's Series; 8 Laurent's Series; 9 Residues: Cauchy's Residue Theorem; 10 Singular Points of an Analytic Function; 11 The Point at Infinity; 12 Evaluation of Residues; 13 Liouville's Theorem; 14 Evaluation of Definite Integrals; 15 Jordan's Lemma16 Bromwich Contour Integrals17 Integrals Involving Multiple-valued Functions (Branch Points); 18 Further Examples of Contour Integrals Around Branch Points; 19 The Use of z and in the Theory of Complex Variables; Problems; References; Chapter 2 Linear Differential Equations; 1 Introduction; 2 The Reduced Equation; the Complementary Function; 3 Properties of the Operator Ln(D); 4 The Method of Partial Fractions; 5 Linear Dependence: Wronskian; 6 The Method of Undetermined Coefficients; 7 The Use of Complex Numbers to Find the Particular Integral8 Linear Second-order Differential Equations with variable Coefficients9 The Method of Frobenius; 10 Variation of Parameters; 11 The Sturm-Liouville Differential Equation; Problems; References; Chapter 3 Linear Algebraic Equations, Determinants, and Matrices; 1 Introduction; 2 Simple Determinants; 3 Fundamental Definitions; 4 Laplace Expansion; 5 Fundamental Properties of Determinants; 6 The Evaluation of Numerical Determinants; 7 Definition of a Matrix; 8 Special Matrices; 9 Equality of Matrices; Addition and Subtraction; 10 Multiplication of Matrices; 11 Matrix Division, the Inverse Matrix12 The Reversal Law in Transposed and Reciprocated Products13 Properties of Diagonal and Unit Matrices; 14 Matrices Partitioned into Submatrices; 15 Matrices of Special Types; 16 The Solution of Linear Algebraic Equations; 17 The Special Case of n Equations and n Unknowns; 18 Systems of Homogeneous Linear Equations; 19 The Characteristic Matrix and the Characteristic Equation of a Matrix; 20 Eigenvalues and the Reduction of a Matrix to Diagonal Form; 21 The Trace of a Matrix; 22 The Cayley-Hamilton Theorem; 23 The Inversion of Large Matrices; 24 Sylvester's Theorem25 Power Series of Matrices Functions of Matrices; 26 Alternate Method of Evaluating Functions of Matrices; 27 Differentiation and Integration of Matrices; 28 Association of Matrices with Linear Differential Equations; 29 Method of Peano-Baker; 30 Adjoint Method; 31 Existence and Uniqueness of Solutions of Matrix Differential Equations; 32 Linear Equations with Periodic Coefficients; 33 Matrix Solution of the Hill-Meissner Equation; 34 The Use of Matrices to Determine the Roots of Algebraic Equations; Problems; References; Chapter 4 Laplace Transforms; 1 Introduction2 The Fourier-Mellin TheoremOne of the most widely used reference books on applied mathematics for a generation, distributed in multiple languages throughout the world, this text is geared toward use with a one-year advanced course in applied mathematics for engineering students. The treatment assumes a solid background in the theory of complex variables and a familiarity with complex numbers, but it includes a brief review. Chapters are as self-contained as possible, offering instructors flexibility in designing their own courses. The first eight chapters explore the analysis of lumped parameter systems. Succeeding topiDover Books on MathematicsMathematical physicsMechanics, AppliedMathematical physicsMechanics, AppliedCivil & Environmental EngineeringHILCCEngineering & Applied SciencesHILCCOperations ResearchHILCCMathematical physics.Mechanics, Applied.Mathematical physics.Mechanics, Applied.Civil & Environmental EngineeringEngineering & Applied SciencesOperations Research510.24/53510.2453Pipes Louis A(Louis Albert),1910-1971.28709Harvill Lawrence R.1935-1824237AU-PeELAU-PeELAU-PeELBOOK9911006987703321Applied Mathematics for Engineers and Physicists4391339UNINA