Advanced Engineering Mathematics, International Student Version

Häftad, Engelska, 2011

Av Erwin Kreyszig, Erwin (Ohio State University) Kreyszig

989 kr

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This market-leading text is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, and self contained subject matter parts for maximum flexibility. The new edition continues with the tradition of providing instructors and students with a comprehensive and up-to-date resource for teaching and learning engineering mathematics, that is, applied mathematics for engineers and physicists, mathematicians and computer scientists, as well as members of other disciplines. This edition can be accompanied with WileyPLUS 5.0, a powerful online teaching and learning environment that integrates the entire digital textbook with the most effective resources to fit every learning style.

Produktinformation

Utgivningsdatum2011-05-03
Mått205 x 255 x 35 mm
Vikt1 896 g
SpråkEngelska
Antal sidor1 152
Upplaga10
FörlagJohn Wiley & Sons Inc
EAN9780470646137

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PART A Ordinary Differential Equations (ODEs) 1CHAPTER 1 First-Order ODEs 21.1 Basic Concepts. Modeling 21.2 Geometric Meaning of y ƒ(x, y). Direction Fields, Euler’s Method 91.3 Separable ODEs. Modeling 121.4 Exact ODEs. Integrating Factors 201.5 Linear ODEs. Bernoulli Equation. Population Dynamics 271.6 Orthogonal Trajectories. Optional 361.7 Existence and Uniqueness of Solutions for Initial Value Problems 38CHAPTER 2 Second-Order Linear ODEs 462.1 Homogeneous Linear ODEs of Second Order 462.2 Homogeneous Linear ODEs with Constant Coefficients 532.3 Differential Operators. Optional 602.4 Modeling of Free Oscillations of a Mass–Spring System 622.5 Euler–Cauchy Equations 712.6 Existence and Uniqueness of Solutions. Wronskian 742.7 Nonhomogeneous ODEs 792.8 Modeling: Forced Oscillations. Resonance 852.9 Modeling: Electric Circuits 932.10 Solution by Variation of Parameters 99CHAPTER 3 Higher Order Linear ODEs 1053.1 Homogeneous Linear ODEs 1053.2 Homogeneous Linear ODEs with Constant Coefficients 1113.3 Nonhomogeneous Linear ODEs 116CHAPTER 4 Systems of ODEs. Phase Plane. Qualitative Methods 1244.0 For Reference: Basics of Matrices and Vectors 1244.1 Systems of ODEs as Models in Engineering Applications 1304.2 Basic Theory of Systems of ODEs. Wronskian 1374.3 Constant-Coefficient Systems. Phase Plane Method 1404.4 Criteria for Critical Points. Stability 1484.5 Qualitative Methods for Nonlinear Systems 1524.6 Nonhomogeneous Linear Systems of ODEs 160CHAPTER 5 Series Solutions of ODEs. Special Functions 1675.1 Power Series Method 1675.2 Legendre's Equation. Legendre Polynomials Pn(x) 1755.3 Extended Power Series Method: Frobenius Method 1805.4 Bessel’s Equation. Bessel Functions (x) 1875.5 Bessel Functions of the Y (x). General Solution 196CHAPTER 6 Laplace Transforms 2036.1 Laplace Transform. Linearity. First Shifting Theorem (s-Shifting) 2046.2 Transforms of Derivatives and Integrals. ODEs 2116.3 Unit Step Function (Heaviside Function). Second Shifting Theorem (t-Shifting) 2176.4 Short Impulses. Dirac's Delta Function. Partial Fractions 2256.5 Convolution. Integral Equations 2326.6 Differentiation and Integration of Transforms. ODEs with Variable Coefficients 2386.7 Systems of ODEs 2426.8 Laplace Transform: General Formulas 2486.9 Table of Laplace Transforms 249PART B Linear Algebra. Vector Calculus 255CHAPTER 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems 2567.1 Matrices, Vectors: Addition and Scalar Multiplication 2577.2 Matrix Multiplication 2637.3 Linear Systems of Equations. Gauss Elimination 2727.4 Linear Independence. Rank of a Matrix. Vector Space 2827.5 Solutions of Linear Systems: Existence, Uniqueness 2887.6 For Reference: Second- and Third-Order Determinants 2917.7 Determinants. Cramer’s Rule 2937.8 Inverse of a Matrix. Gauss–Jordan Elimination 3017.9 Vector Spaces, Inner Product Spaces. Linear Transformations. Optional 309CHAPTER 8 Linear Algebra: Matrix Eigenvalue Problems 3228.1 The Matrix Eigenvalue Problem. Determining Eigenvalues and Eigenvectors 3238.2 Some Applications of Eigenvalue Problems 3298.3 Symmetric, Skew-Symmetric, and Orthogonal Matrices 3348.4 Eigenbases. Diagonalization. Quadratic Forms 3398.5 Complex Matrices and Forms. Optional 346CHAPTER 9 Vector Differential Calculus. Grad, Div, Curl 3549.1 Vectors in 2-Space and 3-Space 3549.2 Inner Product (Dot Product) 3619.3 Vector Product (Cross Product) 3689.4 Vector and Scalar Functions and Their Fields. Vector Calculus: Derivatives 3759.5 Curves. Arc Length. Curvature. Torsion 3819.6 Calculus Review: Functions of Several Variables. Optional 3929.7 Gradient of a Scalar Field. Directional Derivative 3959.8 Divergence of a Vector Field 4039.9 Curl of a Vector Field 406CHAPTER 10 Vector Integral Calculus. Integral Theorems 41310.1 Line Integrals 41310.2 Path Independence of Line Integrals 41910.3 Calculus Review: Double Integrals. Optional 42610.4 Green’s Theorem in the Plane 43310.5 Surfaces for Surface Integrals 43910.6 Surface Integrals 44310.7 Triple Integrals. Divergence Theorem of Gauss 45210.8 Further Applications of the Divergence Theorem 45810.9 Stokes’s Theorem 463PART C Fourier Analysis. Partial Differential Equations (PDEs) 473CHAPTER 11 Fourier Analysis 47411.1 Fourier Series 47411.2 Arbitrary Period. Even and Odd Functions. Half-Range Expansions 48311.3 Forced Oscillations 49211.4 Approximation by Trigonometric Polynomials 49511.5 Sturm–Liouville Problems. Orthogonal Functions 49811.6 Orthogonal Series. Generalized Fourier Series 50411.7 Fourier Integral 51011.8 Fourier Cosine and Sine Transforms 51811.9 Fourier Transform. Discrete and Fast Fourier Transforms 52211.10 Tables of Transforms 534CHAPTER 12 Partial Differential Equations (PDEs) 54012.1 Basic Concepts of PDEs 54012.2 Modeling: Vibrating String, Wave Equation 54312.3 Solution by Separating Variables. Use of Fourier Series 54512.4 D’Alembert’s Solution of the Wave Equation. Characteristics 55312.5 Modeling: Heat Flow from a Body in Space. Heat Equation 55712.6 Heat Equation: Solution by Fourier Series. Steady Two-Dimensional Heat Problems. Dirichlet Problem 55812.7 Heat Equation: Modeling Very Long Bars. Solution by Fourier Integrals and Transforms 56812.8 Modeling: Membrane, Two-Dimensional Wave Equation 57512.9 Rectangular Membrane. Double Fourier Series 57712.10 Laplacian in Polar Coordinates. Circular Membrane. Fourier–Bessel Series 58512.11 Laplace’s Equation in Cylindrical and Spherical Coordinates. Potential 59312.12 Solution of PDEs by Laplace Transforms 600PART D Complex Analysis 607CHAPTER 13 Complex Numbers and Functions. Complex Differentiation 60813.1 Complex Numbers and Their Geometric Representation 60813.2 Polar Form of Complex Numbers. Powers and Roots 61313.3 Derivative. Analytic Function 61913.4 Cauchy–Riemann Equations. Laplace’s Equation 62513.5 Exponential Function 63013.6 Trigonometric and Hyperbolic Functions. Euler's Formula 63313.7 Logarithm. General Power. Principal Value 636CHAPTER 14 Complex Integration 64314.1 Line Integral in the Complex Plane 64314.2 Cauchy's Integral Theorem 65214.3 Cauchy's Integral Formula 66014.4 Derivatives of Analytic Functions 664CHAPTER 15 Power Series, Taylor Series 67115.1 Sequences, Series, Convergence Tests 67115.2 Power Series 68015.3 Functions Given by Power Series 68515.4 Taylor and Maclaurin Series 69015.5 Uniform Convergence. Optional 698CHAPTER 16 Laurent Series. Residue Integration 70816.1 Laurent Series 70816.2 Singularities and Zeros. Infinity 71416.3 Residue Integration Method 71916.4 Residue Integration of Real Integrals 725CHAPTER 17 Conformal Mapping 73517.1 Geometry of Analytic Functions: Conformal Mapping 73617.2 Linear Fractional Transformations (Möbius Transformations) 74117.3 Special Linear Fractional Transformations 74517.4 Conformal Mapping by Other Functions 74917.5 Riemann Surfaces. Optional 753CHAPTER 18 Complex Analysis and Potential Theory 75618.1 Electrostatic Fields 75718.2 Use of Conformal Mapping. Modeling 76118.3 Heat Problems 76518.4 Fluid Flow 76818.5 Poisson's Integral Formula for Potentials 77418.6 General Properties of Harmonic Functions. Uniqueness Theorem for the Dirichlet Problem 778PART E Numeric Analysis 785Software 786CHAPTER 19 Numerics in General 78819.1 Introduction 78819.2 Solution of Equations by Iteration 79519.3 Interpolation 80519.4 Spline Interpolation 81719.5 Numeric Integration and Differentiation 824CHAPTER 20 Numeric Linear Algebra 84120.1 Linear Systems: Gauss Elimination 84120.2 Linear Systems: LU-Factorization, Matrix Inversion 84920.3 Linear Systems: Solution by Iteration 85520.4 Linear Systems: Ill-Conditioning, Norms 86120.5 Least Squares Method 86920.6 Matrix Eigenvalue Problems: Introduction 87320.7 Inclusion of Matrix Eigenvalues 87620.8 Power Method for Eigenvalues 88220.9 Tridiagonalization and QR-Factorization 885CHAPTER 21 Numerics for ODEs and PDEs 89721.1 Methods for First-Order ODEs 89821.2 Multistep Methods 90821.3 Methods for Systems and Higher Order ODEs 91221.4 Methods for Elliptic PDEs 91921.5 Neumann and Mixed Problems. Irregular Boundary 92821.6 Methods for Parabolic PDEs 93321.7 Method for Hyperbolic PDEs 939PART F Optimization, Graphs 947CHAPTER 22 Unconstrained Optimization. Linear Programming 94822.1 Basic Concepts. Unconstrained Optimization: Method of Steepest Descent 94922.2 Linear Programming 95222.3 Simplex Method 95622.4 Simplex Method: Difficulties 960CHAPTER 23 Graphs. Combinatorial Optimization 96723.1 Graphs and Digraphs 96723.2 Shortest Path Problems. Complexity 97223.3 Bellman's Principle. Dijkstra’s Algorithm 97723.4 Shortest Spanning Trees: Greedy Algorithm 98023.5 Shortest Spanning Trees: Prim’s Algorithm 98423.6 Flows in Networks 98723.7 Maximum Flow: Ford–Fulkerson Algorithm 99323.8 Bipartite Graphs. Assignment Problems 996APPENDIX 1 References A1APPENDIX 2 Answers to Selected Problems A4APPENDIX 3 Auxiliary Material A51A3.1 Formulas for Special Functions A51A3.2 Partial Derivatives A57A3.3 Sequences and Series A60A3.4 Grad, Div, Curl, 2 in Curvilinear Coordinates A62APPENDIX 4 Additional Proofs A65APPENDIX 5 Tables A85INDEX I1PHOTO CREDITS P1

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