{"product_id":"advanced-engineering-mathematics-9781119455929","title":"Advanced Engineering Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003ePart A Ordinary Differential Equations (ODEs) \u003c\/b\u003e\u003cb\u003e1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1 First-Order ODEs 2\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Basic Concepts. Modeling 2\u003c\/p\u003e \u003cp\u003e1.2 Geometric Meaning of \u003ci\u003ey\u003c\/i\u003e’= ƒ(\u003ci\u003ex\u003c\/i\u003e, \u003ci\u003ey\u003c\/i\u003e). Direction Fields, Euler’s Method 9\u003c\/p\u003e \u003cp\u003e1.3 Separable ODEs. Modeling 12\u003c\/p\u003e \u003cp\u003e1.4 Exact ODEs. Integrating Factors 20\u003c\/p\u003e \u003cp\u003e1.5 Linear ODEs. Bernoulli Equation. Population Dynamics 27\u003c\/p\u003e \u003cp\u003e1.6 Orthogonal Trajectories. \u003ci\u003eOptional \u003c\/i\u003e36\u003c\/p\u003e \u003cp\u003e1.7 Existence and Uniqueness of Solutions for Initial Value Problems 38\u003c\/p\u003e \u003cp\u003eChapter 1 Review Questions and Problems 43\u003c\/p\u003e \u003cp\u003eSummary of Chapter 1 44\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2 Second-Order Linear ODEs 46\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Homogeneous Linear ODEs of Second Order 46\u003c\/p\u003e \u003cp\u003e2.2 Homogeneous Linear ODEs with Constant Coefficients 53\u003c\/p\u003e \u003cp\u003e2.3 Differential Operators. \u003ci\u003eOptional \u003c\/i\u003e60\u003c\/p\u003e \u003cp\u003e2.4 Modeling of Free Oscillations of a Mass–Spring System 62\u003c\/p\u003e \u003cp\u003e2.5 Euler–Cauchy Equations 71\u003c\/p\u003e \u003cp\u003e2.6 Existence and Uniqueness of Solutions. Wronskian 74\u003c\/p\u003e \u003cp\u003e2.7 Nonhomogeneous ODEs 79\u003c\/p\u003e \u003cp\u003e2.8 Modeling: Forced Oscillations. Resonance 85\u003c\/p\u003e \u003cp\u003e2.9 Modeling: Electric Circuits 93\u003c\/p\u003e \u003cp\u003e2.10 Solution by Variation of Parameters 99\u003c\/p\u003e \u003cp\u003eChapter 2 Review Questions and Problems 102\u003c\/p\u003e \u003cp\u003eSummary of Chapter 2 103\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3 Higher Order Linear ODEs 105\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Homogeneous Linear ODEs 105\u003c\/p\u003e \u003cp\u003e3.2 Homogeneous Linear ODEs with Constant Coefficients 111\u003c\/p\u003e \u003cp\u003e3.3 Nonhomogeneous Linear ODEs 116\u003c\/p\u003e \u003cp\u003eChapter 3 Review Questions and Problems 122\u003c\/p\u003e \u003cp\u003eSummary of Chapter 3 123\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4 Systems of ODEs. Phase Plane. Qualitative Methods 124\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.0 For Reference: Basics of Matrices and Vectors 124\u003c\/p\u003e \u003cp\u003e4.1 Systems of ODEs as Models in Engineering Applications 130\u003c\/p\u003e \u003cp\u003e4.2 Basic Theory of Systems of ODEs. Wronskian 137\u003c\/p\u003e \u003cp\u003e4.3 Constant-Coefficient Systems. Phase Plane Method 140\u003c\/p\u003e \u003cp\u003e4.4 Criteria for Critical Points. Stability 148\u003c\/p\u003e \u003cp\u003e4.5 Qualitative Methods for Nonlinear Systems 152\u003c\/p\u003e \u003cp\u003e4.6 Nonhomogeneous Linear Systems of ODEs 160\u003c\/p\u003e \u003cp\u003eChapter 4 Review Questions and Problems 164\u003c\/p\u003e \u003cp\u003eSummary of Chapter 4 165\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5 Series Solutions of ODEs. Special Functions 167\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Power Series Method 167\u003c\/p\u003e \u003cp\u003e5.2 Legendre’s Equation. Legendre Polynomials \u003ci\u003eP\u003csub\u003en\u003c\/sub\u003e\u003c\/i\u003e(\u003ci\u003ex\u003c\/i\u003e) 175\u003c\/p\u003e \u003cp\u003e5.3 Extended Power Series Method: Frobenius Method 180\u003c\/p\u003e \u003cp\u003e5.4 Bessel’s Equation. Bessel Functions \u003ci\u003eJ\u003c\/i\u003e\u003ci\u003e\u003csub\u003ev\u003c\/sub\u003e\u003c\/i\u003e(\u003ci\u003ex\u003c\/i\u003e) 187\u003c\/p\u003e \u003cp\u003e5.5 Bessel Functions of the \u003ci\u003eY\u003c\/i\u003e\u003ci\u003e\u003csub\u003ev\u003c\/sub\u003e\u003c\/i\u003e(\u003ci\u003ex\u003c\/i\u003e). General Solution 196\u003c\/p\u003e \u003cp\u003eChapter 5 Review Questions and Problems 200\u003c\/p\u003e \u003cp\u003eSummary of Chapter 5 201\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6 Laplace Transforms 203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Laplace Transform. Linearity. First Shifting Theorem (\u003ci\u003es\u003c\/i\u003e-Shifting) 204\u003c\/p\u003e \u003cp\u003e6.2 Transforms of Derivatives and Integrals. ODEs 211\u003c\/p\u003e \u003cp\u003e6.3 Unit Step Function (Heaviside Function). Second Shifting Theorem (\u003ci\u003et\u003c\/i\u003e-Shifting) 217\u003c\/p\u003e \u003cp\u003e6.4 Short Impulses. Dirac’s Delta Function. Partial Fractions 225\u003c\/p\u003e \u003cp\u003e6.5 Convolution. Integral Equations 232\u003c\/p\u003e \u003cp\u003e6.6 Differentiation and Integration of Transforms. ODEs with Variable Coefficients 238\u003c\/p\u003e \u003cp\u003e6.7 Systems of ODEs 242\u003c\/p\u003e \u003cp\u003e6.8 Laplace Transform: General Formulas 248\u003c\/p\u003e \u003cp\u003e6.9 Table of Laplace Transforms 249\u003c\/p\u003e \u003cp\u003eChapter 6 Review Questions and Problems 251\u003c\/p\u003e \u003cp\u003eSummary of Chapter 6 253\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart B Linear Algebra. Vector Calculus \u003c\/b\u003e\u003cb\u003e255\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems 256\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Matrices, Vectors: Addition and Scalar Multiplication 257\u003c\/p\u003e \u003cp\u003e7.2 Matrix Multiplication 263\u003c\/p\u003e \u003cp\u003e7.3 Linear Systems of Equations. Gauss Elimination 272\u003c\/p\u003e \u003cp\u003e7.4 Linear Independence. Rank of a Matrix. Vector Space 282\u003c\/p\u003e \u003cp\u003e7.5 Solutions of Linear Systems: Existence, Uniqueness 288\u003c\/p\u003e \u003cp\u003e7.6 For Reference: Second- and Third-Order Determinants 291\u003c\/p\u003e \u003cp\u003e7.7 Determinants. Cramer’s Rule 293\u003c\/p\u003e \u003cp\u003e7.8 Inverse of a Matrix. Gauss–Jordan Elimination 301\u003c\/p\u003e \u003cp\u003e7.9 Vector Spaces, Inner Product Spaces. Linear Transformations. \u003ci\u003eOptional \u003c\/i\u003e309\u003c\/p\u003e \u003cp\u003eChapter 7 Review Questions and Problems 318\u003c\/p\u003e \u003cp\u003eSummary of Chapter 7 320\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8 Linear Algebra: Matrix Eigenvalue Problems 322\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 The Matrix Eigenvalue Problem. Determining Eigenvalues and Eigenvectors 323\u003c\/p\u003e \u003cp\u003e8.2 Some Applications of Eigenvalue Problems 329\u003c\/p\u003e \u003cp\u003e8.3 Symmetric, Skew-Symmetric, and Orthogonal Matrices 334\u003c\/p\u003e \u003cp\u003e8.4 Eigenbases. Diagonalization. Quadratic Forms 339\u003c\/p\u003e \u003cp\u003e8.5 Complex Matrices and Forms. \u003ci\u003eOptional \u003c\/i\u003e346\u003c\/p\u003e \u003cp\u003eChapter 8 Review Questions and Problems 352\u003c\/p\u003e \u003cp\u003eSummary of Chapter 8 353\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9 Vector Differential Calculus. Grad, Div, Curl 354\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Vectors in 2-Space and 3-Space 354\u003c\/p\u003e \u003cp\u003e9.2 Inner Product (Dot Product) 361\u003c\/p\u003e \u003cp\u003e9.3 Vector Product (Cross Product) 368\u003c\/p\u003e \u003cp\u003e9.4 Vector and Scalar Functions and Their Fields. Vector Calculus: Derivatives 375\u003c\/p\u003e \u003cp\u003e9.5 Curves. Arc Length. Curvature. Torsion 381\u003c\/p\u003e \u003cp\u003e9.6 Calculus Review: Functions of Several Variables. \u003ci\u003eOptional \u003c\/i\u003e392\u003c\/p\u003e \u003cp\u003e9.7 Gradient of a Scalar Field. Directional Derivative 395\u003c\/p\u003e \u003cp\u003e9.8 Divergence of a Vector Field 403\u003c\/p\u003e \u003cp\u003e9.9 Curl of a Vector Field 406\u003c\/p\u003e \u003cp\u003eChapter 9 Review Questions and Problems 409\u003c\/p\u003e \u003cp\u003eSummary of Chapter 9 410\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 10 Vector Integral Calculus. Integral Theorems 413\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Line Integrals 413\u003c\/p\u003e \u003cp\u003e10.2 Path Independence of Line Integrals 419\u003c\/p\u003e \u003cp\u003e10.3 Calculus Review: Double Integrals. \u003ci\u003eOptional \u003c\/i\u003e426\u003c\/p\u003e \u003cp\u003e10.4 Green’s Theorem in the Plane 433\u003c\/p\u003e \u003cp\u003e10.5 Surfaces for Surface Integrals 439\u003c\/p\u003e \u003cp\u003e10.6 Surface Integrals 443\u003c\/p\u003e \u003cp\u003e10.7 Triple Integrals. Divergence Theorem of Gauss 452\u003c\/p\u003e \u003cp\u003e10.8 Further Applications of the Divergence Theorem 458\u003c\/p\u003e \u003cp\u003e10.9 Stokes’s Theorem 463\u003c\/p\u003e \u003cp\u003eChapter 10 Review Questions and Problems 469\u003c\/p\u003e \u003cp\u003eSummary of Chapter 10 470\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart C Fourier Analysis. Partial Differential Equations (PDEs) \u003c\/b\u003e\u003cb\u003e473\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 11 Fourier Analysis 474\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Fourier Series 474\u003c\/p\u003e \u003cp\u003e11.2 Arbitrary Period. Even and Odd Functions. Half-Range Expansions 483\u003c\/p\u003e \u003cp\u003e11.3 Forced Oscillations 492\u003c\/p\u003e \u003cp\u003e11.4 Approximation by Trigonometric Polynomials 495\u003c\/p\u003e \u003cp\u003e11.5 Sturm–Liouville Problems. Orthogonal Functions 498\u003c\/p\u003e \u003cp\u003e11.6 Orthogonal Series. Generalized Fourier Series 504\u003c\/p\u003e \u003cp\u003e11.7 Fourier Integral 510\u003c\/p\u003e \u003cp\u003e11.8 Fourier Cosine and Sine Transforms 518\u003c\/p\u003e \u003cp\u003e11.9 Fourier Transform. Discrete and Fast Fourier Transforms 522\u003c\/p\u003e \u003cp\u003e11.10 Tables of Transforms 534\u003c\/p\u003e \u003cp\u003eChapter 11 Review Questions and Problems 537\u003c\/p\u003e \u003cp\u003eSummary of Chapter 11 538\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 12 Partial Differential Equations (PDEs) 540\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Basic Concepts of PDEs 540\u003c\/p\u003e \u003cp\u003e12.2 Modeling: Vibrating String, Wave Equation 543\u003c\/p\u003e \u003cp\u003e12.3 Solution by Separating Variables. Use of Fourier Series 545\u003c\/p\u003e \u003cp\u003e12.4 D’Alembert’s Solution of the Wave Equation. Characteristics 553\u003c\/p\u003e \u003cp\u003e12.5 Modeling: Heat Flow from a Body in Space. Heat Equation 557\u003c\/p\u003e \u003cp\u003e12.6 Heat Equation: Solution by Fourier Series. Steady Two-Dimensional Heat Problems. Dirichlet Problem 558\u003c\/p\u003e \u003cp\u003e12.7 Heat Equation: Modeling Very Long Bars. Solution by Fourier Integrals and Transforms 568\u003c\/p\u003e \u003cp\u003e12.8 Modeling: Membrane, Two-Dimensional Wave Equation 575\u003c\/p\u003e \u003cp\u003e12.9 Rectangular Membrane. Double Fourier Series 577\u003c\/p\u003e \u003cp\u003e12.10 Laplacian in Polar Coordinates. Circular Membrane. Fourier–Bessel Series 585\u003c\/p\u003e \u003cp\u003e12.11 Laplace’s Equation in Cylindrical and Spherical Coordinates. Potential 593\u003c\/p\u003e \u003cp\u003e12.12 Solution of PDEs by Laplace Transforms 600\u003c\/p\u003e \u003cp\u003eChapter 12 Review Questions and Problems 603\u003c\/p\u003e \u003cp\u003eSummary of Chapter 12 604\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart D Complex Analysis \u003c\/b\u003e\u003cb\u003e607\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 13 Complex Numbers and Functions. Complex Differentiation 608\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Complex Numbers and Their Geometric Representation 608\u003c\/p\u003e \u003cp\u003e13.2 Polar Form of Complex Numbers. Powers and Roots 613\u003c\/p\u003e \u003cp\u003e13.3 Derivative. Analytic Function 619\u003c\/p\u003e \u003cp\u003e13.4 Cauchy–Riemann Equations. Laplace’s Equation 625\u003c\/p\u003e \u003cp\u003e13.5 Exponential Function 630\u003c\/p\u003e \u003cp\u003e13.6 Trigonometric and Hyperbolic Functions. Euler’s Formula 633\u003c\/p\u003e \u003cp\u003e13.7 Logarithm. General Power. Principal Value 636\u003c\/p\u003e \u003cp\u003eChapter 13 Review Questions and Problems 641\u003c\/p\u003e \u003cp\u003eSummary of Chapter 13 641\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 14 Complex Integration 643\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Line Integral in the Complex Plane 643\u003c\/p\u003e \u003cp\u003e14.2 Cauchy’s Integral Theorem 652\u003c\/p\u003e \u003cp\u003e14.3 Cauchy’s Integral Formula 660\u003c\/p\u003e \u003cp\u003e14.4 Derivatives of Analytic Functions 664\u003c\/p\u003e \u003cp\u003eChapter 14 Review Questions and Problems 668\u003c\/p\u003e \u003cp\u003eSummary of Chapter 14 669\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 15 Power Series, Taylor Series 671\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Sequences, Series, Convergence Tests 671\u003c\/p\u003e \u003cp\u003e15.2 Power Series 680\u003c\/p\u003e \u003cp\u003e15.3 Functions Given by Power Series 685\u003c\/p\u003e \u003cp\u003e15.4 Taylor and Maclaurin Series 690\u003c\/p\u003e \u003cp\u003e15.5 Uniform Convergence. \u003ci\u003eOptional \u003c\/i\u003e698\u003c\/p\u003e \u003cp\u003eChapter 15 Review Questions and Problems 706\u003c\/p\u003e \u003cp\u003eSummary of Chapter 15 706\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 16 Laurent Series. Residue Integration 708\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Laurent Series 708\u003c\/p\u003e \u003cp\u003e16.2 Singularities and Zeros. Infinity 715\u003c\/p\u003e \u003cp\u003e16.3 Residue Integration Method 719\u003c\/p\u003e \u003cp\u003e16.4 Residue Integration of Real Integrals 725\u003c\/p\u003e \u003cp\u003eChapter 16 Review Questions and Problems 733\u003c\/p\u003e \u003cp\u003eSummary of Chapter 16 734\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 17 Conformal Mapping 736\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Geometry of Analytic Functions: Conformal Mapping 737\u003c\/p\u003e \u003cp\u003e17.2 Linear Fractional Transformations (Möbius Transformations) 742\u003c\/p\u003e \u003cp\u003e17.3 Special Linear Fractional Transformations 746\u003c\/p\u003e \u003cp\u003e17.4 Conformal Mapping by Other Functions 750\u003c\/p\u003e \u003cp\u003e17.5 Riemann Surfaces. \u003ci\u003eOptional \u003c\/i\u003e754\u003c\/p\u003e \u003cp\u003eChapter 17 Review Questions and Problems 756\u003c\/p\u003e \u003cp\u003eSummary of Chapter 17 757\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 18 Complex Analysis and Potential Theory 758\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Electrostatic Fields 759\u003c\/p\u003e \u003cp\u003e18.2 Use of Conformal Mapping. Modeling 763\u003c\/p\u003e \u003cp\u003e18.3 Heat Problems 767\u003c\/p\u003e \u003cp\u003e18.4 Fluid Flow 771\u003c\/p\u003e \u003cp\u003e18.5 Poisson’s Integral Formula for Potentials 777\u003c\/p\u003e \u003cp\u003e18.6 General Properties of Harmonic Functions. Uniqueness Theorem for the Dirichlet Problem 781\u003c\/p\u003e \u003cp\u003eChapter 18 Review Questions and Problems 785\u003c\/p\u003e \u003cp\u003eSummary of Chapter 18 786\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart E Numeric Analysis \u003c\/b\u003e\u003cb\u003e787\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSoftware \u003c\/b\u003e\u003cb\u003e788\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 19 Numerics in General 790\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Introduction 790\u003c\/p\u003e \u003cp\u003e19.2 Solution of Equations by Iteration 798\u003c\/p\u003e \u003cp\u003e19.3 Interpolation 808\u003c\/p\u003e \u003cp\u003e19.4 Spline Interpolation 820\u003c\/p\u003e \u003cp\u003e19.5 Numeric Integration and Differentiation 827\u003c\/p\u003e \u003cp\u003eChapter 19 Review Questions and Problems 841\u003c\/p\u003e \u003cp\u003eSummary of Chapter 19 842\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 20 Numeric Linear Algebra 844\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 Linear Systems: Gauss Elimination 844\u003c\/p\u003e \u003cp\u003e20.2 Linear Systems: LU-Factorization, Matrix Inversion 852\u003c\/p\u003e \u003cp\u003e20.3 Linear Systems: Solution by Iteration 858\u003c\/p\u003e \u003cp\u003e20.4 Linear Systems: Ill-Conditioning, Norms 864\u003c\/p\u003e \u003cp\u003e20.5 Least Squares Method 872\u003c\/p\u003e \u003cp\u003e20.6 Matrix Eigenvalue Problems: Introduction 876\u003c\/p\u003e \u003cp\u003e20.7 Inclusion of Matrix Eigenvalues 879\u003c\/p\u003e \u003cp\u003e20.8 Power Method for Eigenvalues 885\u003c\/p\u003e \u003cp\u003e20.9 Tridiagonalization and QR-Factorization 888\u003c\/p\u003e \u003cp\u003eChapter 20 Review Questions and Problems 896\u003c\/p\u003e \u003cp\u003eSummary of Chapter 20 898\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 21 Numerics for ODEs and PDEs 900\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21.1 Methods for First-Order ODEs 901\u003c\/p\u003e \u003cp\u003e21.2 Multistep Methods 911\u003c\/p\u003e \u003cp\u003e21.3 Methods for Systems and Higher Order ODEs 915\u003c\/p\u003e \u003cp\u003e21.4 Methods for Elliptic PDEs 922\u003c\/p\u003e \u003cp\u003e21.5 Neumann and Mixed Problems. Irregular Boundary 931\u003c\/p\u003e \u003cp\u003e21.6 Methods for Parabolic PDEs 936\u003c\/p\u003e \u003cp\u003e21.7 Method for Hyperbolic PDEs 942\u003c\/p\u003e \u003cp\u003eChapter 21 Review Questions and Problems 945\u003c\/p\u003e \u003cp\u003eSummary of Chapter 21 946\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart F Optimization, Graphs \u003c\/b\u003e\u003cb\u003e949\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 22 Unconstrained Optimization. Linear Programming 950\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e22.1 Basic Concepts. Unconstrained Optimization: Method of Steepest Descent 951\u003c\/p\u003e \u003cp\u003e22.2 Linear Programming 954\u003c\/p\u003e \u003cp\u003e22.3 Simplex Method 958\u003c\/p\u003e \u003cp\u003e22.4 Simplex Method: Difficulties 962\u003c\/p\u003e \u003cp\u003eChapter 22 Review Questions and Problems 968\u003c\/p\u003e \u003cp\u003eSummary of Chapter 22 969\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 23 Graphs. Combinatorial Optimization 970\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e23.1 Graphs and Digraphs 970\u003c\/p\u003e \u003cp\u003e23.2 Shortest Path Problems. Complexity 975\u003c\/p\u003e \u003cp\u003e23.3 Bellman’s Principle. Dijkstra’s Algorithm 980\u003c\/p\u003e \u003cp\u003e23.4 Shortest Spanning Trees: Greedy Algorithm 984\u003c\/p\u003e \u003cp\u003e23.5 Shortest Spanning Trees: Prim’s Algorithm 988\u003c\/p\u003e \u003cp\u003e23.6 Flows in Networks 991\u003c\/p\u003e \u003cp\u003e23.7 Maximum Flow: Ford–Fulkerson Algorithm 998\u003c\/p\u003e \u003cp\u003e23.8 Bipartite Graphs. Assignment Problems 1001\u003c\/p\u003e \u003cp\u003eChapter 23 Review Questions and Problems 1006\u003c\/p\u003e \u003cp\u003eSummary of Chapter 23 1007\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart G Probability, Statistics \u003c\/b\u003e\u003cb\u003e1009\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSoftware \u003c\/b\u003e\u003cb\u003e1009\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 24 Data Analysis. Probability Theory 1011\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e24.1 Data Representation. Average. Spread 1011\u003c\/p\u003e \u003cp\u003e24.2 Experiments, Outcomes, Events 1015\u003c\/p\u003e \u003cp\u003e24.3 Probability 1018\u003c\/p\u003e \u003cp\u003e24.4 Permutations and Combinations 1024\u003c\/p\u003e \u003cp\u003e24.5 Random Variables. Probability Distributions 1029\u003c\/p\u003e \u003cp\u003e24.6 Mean and Variance of a Distribution 1035\u003c\/p\u003e \u003cp\u003e24.7 Binomial, Poisson, and Hypergeometric Distributions 1039\u003c\/p\u003e \u003cp\u003e24.8 Normal Distribution 1045\u003c\/p\u003e \u003cp\u003e24.9 Distributions of Several Random Variables 1051\u003c\/p\u003e \u003cp\u003eChapter 24 Review Questions and Problems 1060\u003c\/p\u003e \u003cp\u003eSummary of Chapter 24 1060\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 25 Mathematical Statistics 1063\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e25.1 Introduction. Random Sampling 1063\u003c\/p\u003e \u003cp\u003e25.2 Point Estimation of Parameters 1065\u003c\/p\u003e \u003cp\u003e25.3 Confidence Intervals 1068\u003c\/p\u003e \u003cp\u003e25.4 Testing Hypotheses. Decisions 1077\u003c\/p\u003e \u003cp\u003e25.5 Quality Control 1087\u003c\/p\u003e \u003cp\u003e25.6 Acceptance Sampling 1092\u003c\/p\u003e \u003cp\u003e25.7 Goodness of Fit. χ\u003csup\u003e2\u003c\/sup\u003e -Test 1096\u003c\/p\u003e \u003cp\u003e25.8 Nonparametric Tests 1100\u003c\/p\u003e \u003cp\u003e25.9 Regression. Fitting Straight Lines. Correlation 1103\u003c\/p\u003e \u003cp\u003eChapter 25 Review Questions and Problems 1111\u003c\/p\u003e \u003cp\u003eSummary of Chapter 25 1112\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix 1 References A1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix 2 Answers to Odd-Numbered Problems A4\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix 3 Auxiliary Material A63\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA3.1 Formulas for Special Functions A63\u003c\/p\u003e \u003cp\u003eA3.2 Partial Derivatives A69\u003c\/p\u003e \u003cp\u003eA3.3 Sequences and Series A72\u003c\/p\u003e \u003cp\u003eA3.4 Grad, Div, Curl, ∇\u003csup\u003e2\u003c\/sup\u003e in Curvilinear Coordinates A74\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix 4 Additional Proofs A77\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix 5 Tables A97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIndex I1\u003c\/p\u003e \u003cp\u003ePhoto Credits P1\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49528855986519,"sku":"9781119455929","price":128.66,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/bookcurl.com\/products\/advanced-engineering-mathematics-9781119455929","provider":"Book Curl","version":"1.0","type":"link"}