{"product_id":"applied-mathematics-for-science-and-engineering-9781118749920","title":"Applied Mathematics for Science and Engineering","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eBased on a decade   s worth of the authors lecture notes detailing the topic of applied mathematics for scientists and engineers. The flow of the chapters is smooth and moves from one mathematical method to the next sustaining reader interest and easing the application of the techniques.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface viii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Problem Formulation and Model Development 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 1\u003c\/p\u003e \u003cp\u003eAlgebraic Equations from Vapor–Liquid Equilibria (VLE) 3\u003c\/p\u003e \u003cp\u003eMacroscopic Balances: Lumped-Parameter Models 4\u003c\/p\u003e \u003cp\u003eForce Balances: Newton’s Second Law of Motion 6\u003c\/p\u003e \u003cp\u003eDistributed Parameter Models: Microscopic Balances 6\u003c\/p\u003e \u003cp\u003eUsing the Equations of Change Directly 8\u003c\/p\u003e \u003cp\u003eA Contrast: Deterministic Models and Stochastic Processes 10\u003c\/p\u003e \u003cp\u003eEmpiricisms and Data Interpretation 10\u003c\/p\u003e \u003cp\u003eConclusion 12\u003c\/p\u003e \u003cp\u003eProblems 13\u003c\/p\u003e \u003cp\u003eReferences 14\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Algebraic Equations 15\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 15\u003c\/p\u003e \u003cp\u003eElementary Methods 16\u003c\/p\u003e \u003cp\u003eNewton–Raphson (Newton’s Method of Tangents) 16\u003c\/p\u003e \u003cp\u003eRegula Falsi (False Position Method) 18\u003c\/p\u003e \u003cp\u003eDichotomous Search 19\u003c\/p\u003e \u003cp\u003eGolden Section Search 20\u003c\/p\u003e \u003cp\u003eSimultaneous Linear Algebraic Equations 20\u003c\/p\u003e \u003cp\u003eCrout’s (or Cholesky’s) Method 21\u003c\/p\u003e \u003cp\u003eMatrix Inversion 23\u003c\/p\u003e \u003cp\u003eIterative Methods of Solution 23\u003c\/p\u003e \u003cp\u003eSimultaneous Nonlinear Algebraic Equations 24\u003c\/p\u003e \u003cp\u003ePattern Search for Solution of Nonlinear Algebraic Equations 26\u003c\/p\u003e \u003cp\u003eSequential Simplex and the Rosenbrock Method 26\u003c\/p\u003e \u003cp\u003eAn Example of a Pattern Search Application 28\u003c\/p\u003e \u003cp\u003eAlgebraic Equations with Constraints 28\u003c\/p\u003e \u003cp\u003eConclusion 29\u003c\/p\u003e \u003cp\u003eProblems 30\u003c\/p\u003e \u003cp\u003eReferences 32\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Vectors and Tensors 34\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 34\u003c\/p\u003e \u003cp\u003eManipulation of Vectors 35\u003c\/p\u003e \u003cp\u003eForce Equilibrium 37\u003c\/p\u003e \u003cp\u003eEquating Moments 37\u003c\/p\u003e \u003cp\u003eProjectile Motion 38\u003c\/p\u003e \u003cp\u003eDot and Cross Products 39\u003c\/p\u003e \u003cp\u003eDifferentiation of Vectors 40\u003c\/p\u003e \u003cp\u003eGradient Divergence and Curl 40\u003c\/p\u003e \u003cp\u003eGreen’s Theorem 42\u003c\/p\u003e \u003cp\u003eStokes’ Theorem 43\u003c\/p\u003e \u003cp\u003eConclusion 44\u003c\/p\u003e \u003cp\u003eProblems 44\u003c\/p\u003e \u003cp\u003eReferences 46\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Numerical Quadrature 47\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 47\u003c\/p\u003e \u003cp\u003eTrapezoid Rule 47\u003c\/p\u003e \u003cp\u003eSimpson’s Rule 48\u003c\/p\u003e \u003cp\u003eNewton–Cotes Formulae 49\u003c\/p\u003e \u003cp\u003eRoundoff and Truncation Errors 50\u003c\/p\u003e \u003cp\u003eRomberg Integration 51\u003c\/p\u003e \u003cp\u003eAdaptive Integration Schemes 52\u003c\/p\u003e \u003cp\u003eSimpson’s Rule 52\u003c\/p\u003e \u003cp\u003eGaussian Quadrature and the Gauss–Kronrod Procedure 53\u003c\/p\u003e \u003cp\u003eIntegrating Discrete Data 55\u003c\/p\u003e \u003cp\u003eMultiple Integrals (Cubature) 57\u003c\/p\u003e \u003cp\u003eMonte Carlo Methods 59\u003c\/p\u003e \u003cp\u003eConclusion 60\u003c\/p\u003e \u003cp\u003eProblems 62\u003c\/p\u003e \u003cp\u003eReferences 64\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Analytic Solution of Ordinary Differential Equations 65\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAn Introductory Example 65\u003c\/p\u003e \u003cp\u003eFirst-Order Ordinary Differential Equations 66\u003c\/p\u003e \u003cp\u003eNonlinear First-Order Ordinary Differential Equations 67\u003c\/p\u003e \u003cp\u003eSolutions with Elliptic Integrals and Elliptic Functions 69\u003c\/p\u003e \u003cp\u003eHigher-Order Linear ODEs with Constant Coefficients 71\u003c\/p\u003e \u003cp\u003eUse of the Laplace Transform for Solution of ODEs 73\u003c\/p\u003e \u003cp\u003eHigher-Order Equations with Variable Coefficients 75\u003c\/p\u003e \u003cp\u003eBessel’s Equation and Bessel Functions 76\u003c\/p\u003e \u003cp\u003ePower Series Solutions of Ordinary Differential Equations 78\u003c\/p\u003e \u003cp\u003eRegular Perturbation 80\u003c\/p\u003e \u003cp\u003eLinearization 81\u003c\/p\u003e \u003cp\u003eConclusion 83\u003c\/p\u003e \u003cp\u003eProblems 84\u003c\/p\u003e \u003cp\u003eReferences 88\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Numerical Solution of Ordinary Differential Equations 89\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAn Illustrative Example 89\u003c\/p\u003e \u003cp\u003eThe Euler Method 90\u003c\/p\u003e \u003cp\u003eModified Euler Method 91\u003c\/p\u003e \u003cp\u003eRunge–Kutta Methods 91\u003c\/p\u003e \u003cp\u003eSimultaneous Ordinary Differential Equations 94\u003c\/p\u003e \u003cp\u003eSome Potential Difficulties Illustrated 94\u003c\/p\u003e \u003cp\u003eLimitations of Fixed Step-Size Algorithms 95\u003c\/p\u003e \u003cp\u003eRichardson Extrapolation 97\u003c\/p\u003e \u003cp\u003eMultistep Methods 98\u003c\/p\u003e \u003cp\u003eSplit Boundary Conditions 98\u003c\/p\u003e \u003cp\u003eFinite-Difference Methods 100\u003c\/p\u003e \u003cp\u003eStiff Differential Equations 100\u003c\/p\u003e \u003cp\u003eBackward Differentiation Formula (BDF) Methods 101\u003c\/p\u003e \u003cp\u003eBulirsch–Stoer Method 102\u003c\/p\u003e \u003cp\u003ePhase Space 103\u003c\/p\u003e \u003cp\u003eSummary 105\u003c\/p\u003e \u003cp\u003eProblems 106\u003c\/p\u003e \u003cp\u003eReferences 109\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Analytic Solution of Partial Differential Equations 111\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 111\u003c\/p\u003e \u003cp\u003eClassification of Partial Differential Equations and Boundary Conditions 111\u003c\/p\u003e \u003cp\u003eFourier Series 112\u003c\/p\u003e \u003cp\u003eA Preview of the Utility of Fourier Series 114\u003c\/p\u003e \u003cp\u003eThe Product Method (Separation of Variables) 116\u003c\/p\u003e \u003cp\u003eParabolic Equations 116\u003c\/p\u003e \u003cp\u003eElliptic Equations 122\u003c\/p\u003e \u003cp\u003eApplication to Hyperbolic Equations 127\u003c\/p\u003e \u003cp\u003eThe Schrödinger Equation 128\u003c\/p\u003e \u003cp\u003eApplications of the Laplace Transform 131\u003c\/p\u003e \u003cp\u003eApproximate Solution Techniques 133\u003c\/p\u003e \u003cp\u003eGalerkin MWR Applied to a PDE 134\u003c\/p\u003e \u003cp\u003eThe Rayleigh–Ritz Method 135\u003c\/p\u003e \u003cp\u003eCollocation 137\u003c\/p\u003e \u003cp\u003eOrthogonal Collocation for Partial Differential Equations 138\u003c\/p\u003e \u003cp\u003eThe Cauchy–Riemann Equations Conformal Mapping and Solutions for the Laplace Equation 139\u003c\/p\u003e \u003cp\u003eConclusion 142\u003c\/p\u003e \u003cp\u003eProblems 143\u003c\/p\u003e \u003cp\u003eReferences 146\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Numerical Solution of Partial Differential Equations 147\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 147\u003c\/p\u003e \u003cp\u003eFinite-Difference Approximations for Derivatives 148\u003c\/p\u003e \u003cp\u003eBoundaries with Specified Flux 149\u003c\/p\u003e \u003cp\u003eElliptic Partial Differential Equations 149\u003c\/p\u003e \u003cp\u003eAn Iterative Numerical Procedure: Gauss–Seidel 151\u003c\/p\u003e \u003cp\u003eImproving the Rate of Convergence with Successive Over-Relaxation (SOR) 152\u003c\/p\u003e \u003cp\u003eParabolic Partial Differential Equations 154\u003c\/p\u003e \u003cp\u003eAn Elementary Explicit Numerical Procedure 154\u003c\/p\u003e \u003cp\u003eThe Crank–Nicolson Method 155\u003c\/p\u003e \u003cp\u003eAlternating-Direction Implicit (ADI) Method 157\u003c\/p\u003e \u003cp\u003eThree Spatial Dimensions 158\u003c\/p\u003e \u003cp\u003eHyperbolic Partial Differential Equations 158\u003c\/p\u003e \u003cp\u003eThe Method of Characteristics 160\u003c\/p\u003e \u003cp\u003eThe Leapfrog Method 161\u003c\/p\u003e \u003cp\u003eElementary Problems with Convective Transport 162\u003c\/p\u003e \u003cp\u003eA Numerical Procedure for Two-Dimensional Viscous Flow Problems 165\u003c\/p\u003e \u003cp\u003eMacCormack’s Method 170\u003c\/p\u003e \u003cp\u003eAdaptive Grids 171\u003c\/p\u003e \u003cp\u003eConclusion 173\u003c\/p\u003e \u003cp\u003eProblems 176\u003c\/p\u003e \u003cp\u003eReferences 183\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Integro-Differential Equations 184\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 184\u003c\/p\u003e \u003cp\u003eAn Example of Three-Mode Control 185\u003c\/p\u003e \u003cp\u003ePopulation Problems with Hereditary Infl uences 186\u003c\/p\u003e \u003cp\u003eAn Elementary Solution Strategy 187\u003c\/p\u003e \u003cp\u003eVIM: The Variational Iteration Method 188\u003c\/p\u003e \u003cp\u003eIntegro-Differential Equations and the Spread of Infectious Disease 192\u003c\/p\u003e \u003cp\u003eExamples Drawn from Population Balances 194\u003c\/p\u003e \u003cp\u003eParticle Size in Coagulating Systems 198\u003c\/p\u003e \u003cp\u003eApplication of the Population Balance to a Continuous Crystallizer 199\u003c\/p\u003e \u003cp\u003eConclusion 201\u003c\/p\u003e \u003cp\u003eProblems 201\u003c\/p\u003e \u003cp\u003eReferences 204\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Time-Series Data and the Fourier Transform 206\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIntroduction 206\u003c\/p\u003e \u003cp\u003eA Nineteenth-Century Idea 207\u003c\/p\u003e \u003cp\u003eThe Autocorrelation Coeffi cient 208\u003c\/p\u003e \u003cp\u003eA Fourier Transform Pair 209\u003c\/p\u003e \u003cp\u003eThe Fast Fourier Transform 210\u003c\/p\u003e \u003cp\u003eAliasing and Leakage 213\u003c\/p\u003e \u003cp\u003eSmoothing Data by Filtering 216\u003c\/p\u003e \u003cp\u003eModulation (Beats) 218\u003c\/p\u003e \u003cp\u003eSome Familiar Examples 219\u003c\/p\u003e \u003cp\u003eTurbulent Flow in a Deflected Air Jet 219\u003c\/p\u003e \u003cp\u003eBubbles and the Gas–Liquid Interface 220\u003c\/p\u003e \u003cp\u003eShock and Vibration Events in Transportation 222\u003c\/p\u003e \u003cp\u003eConclusion and Some Final Thoughts 223\u003c\/p\u003e \u003cp\u003eProblems 224\u003c\/p\u003e \u003cp\u003eReferences 227\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 An Introduction to the Calculus of Variations and the Finite-Element Method 229\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSome Preliminaries 229\u003c\/p\u003e \u003cp\u003eNotation for the Calculus of Variations 230\u003c\/p\u003e \u003cp\u003eBrachistochrone Problem 231\u003c\/p\u003e \u003cp\u003eOther Examples 232\u003c\/p\u003e \u003cp\u003eMinimum Surface Area 232\u003c\/p\u003e \u003cp\u003eSystems of Particles 232\u003c\/p\u003e \u003cp\u003eVibrating String 233\u003c\/p\u003e \u003cp\u003eLaplace’s Equation 234\u003c\/p\u003e \u003cp\u003eBoundary-Value Problems 234\u003c\/p\u003e \u003cp\u003eA Contemporary COV Analysis of an Old Structural Problem 236\u003c\/p\u003e \u003cp\u003eFlexing of a Rod of Small Cross Section 236\u003c\/p\u003e \u003cp\u003eThe Optimal Column Shape 237\u003c\/p\u003e \u003cp\u003eSystems with Surface Tension 238\u003c\/p\u003e \u003cp\u003eThe Connection between COV and the Finite-Element Method (FEM) 238\u003c\/p\u003e \u003cp\u003eConclusion 241\u003c\/p\u003e \u003cp\u003eProblems 242\u003c\/p\u003e \u003cp\u003eReferences 243\u003c\/p\u003e \u003cp\u003eIndex 245\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default 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