book

Applied Mathematics for Science and Engineering

by Larry A. Glasgow

September 2014

Intermediate to advanced

256 pages

13h 14m

English

Wiley

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IntroductionAlgebraic Equations from Vapor–Liquid Equilibria (VLE)Macroscopic Balances: Lumped-Parameter ModelsForce Balances: Newton's Second Law of MotionDistributed Parameter Models: Microscopic BalancesA Contrast: Deterministic Models and Stochastic ProcessesEmpiricisms and Data InterpretationConclusionProblemsReferences
IntroductionElementary MethodsSimultaneous Linear Algebraic EquationsSimultaneous Nonlinear Algebraic EquationsAlgebraic Equations with ConstraintsConclusionProblemsReferences
IntroductionManipulation of VectorsGreen's TheoremStokes' TheoremConclusionProblemsReferences
IntroductionTrapezoid RuleSimpson's RuleNewton–Cotes FormulaeRoundoff and Truncation ErrorsRomberg IntegrationAdaptive Integration SchemesIntegrating Discrete DataMultiple Integrals (Cubature)ConclusionProblemsReferences
An Introductory ExampleFirst-Order Ordinary Differential EquationsNonlinear First-Order Ordinary Differential EquationsHigher-Order Linear ODEs with Constant CoefficientsHigher-Order Equations with Variable CoefficientsBessel's Equation and Bessel FunctionsPower Series Solutions of Ordinary Differential EquationsRegular PerturbationLinearizationConclusionProblemsReferences
An Illustrative ExampleThe Euler MethodRunge–Kutta MethodsSimultaneous Ordinary Differential EquationsLimitations of Fixed Step-Size AlgorithmsRichardson ExtrapolationMultistep MethodsSplit Boundary ConditionsFinite-Difference MethodsStiff Differential EquationsBulirsch–Stoer MethodPhase SpaceSummaryProblemsReferences
IntroductionClassification of Partial Differential Equations and Boundary ConditionsFourier SeriesThe Product Method (Separation of Variables)Applications of the Laplace TransformApproximate Solution TechniquesThe Cauchy–Riemann Equations, Conformal Mapping, and Solutions for the Laplace EquationConclusionProblemsReferences

IntroductionElliptic Partial Differential EquationsParabolic Partial Differential EquationsHyperbolic Partial Differential EquationsElementary Problems with Convective TransportA Numerical Procedure for Two-Dimensional Viscous Flow ProblemsMacCormack's MethodAdaptive GridsConclusionProblemsReferences
IntroductionAn Example of Three-Mode ControlPopulation Problems with Hereditary InfluencesAn Elementary Solution StrategyVIM: The Variational Iteration MethodIntegro-Differential Equations and the Spread of Infectious DiseaseExamples Drawn from Population BalancesConclusionProblemsReferences
IntroductionA Nineteenth-Century IdeaThe Autocorrelation CoefficientA Fourier Transform PairThe Fast Fourier TransformAliasing and LeakageSmoothing Data by FilteringModulation (Beats)Some Familiar ExamplesConclusion and Some Final ThoughtsProblemsReferences
Some PreliminariesNotation for the Calculus of VariationsBrachistochrone ProblemOther ExamplesA Contemporary COV Analysis of an Old Structural ProblemSystems with Surface TensionThe Connection between COV and the Finite-Element Method (FEM)ConclusionProblemsNoteReferences

Overview

Prepare students for success in using applied mathematics for engineering practice and post-graduate studies

moves from one mathematical method to the next sustaining reader interest and easing the application of the techniques

Uses different examples from chemical, civil, mechanical and various other engineering fields

Based on a decade's worth of the authors lecture notes detailing the topic of applied mathematics for scientists and engineers

Concisely writing with numerous examples provided including historical perspectives as well as a solutions manual for academic adopters

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Publisher Resources

ISBN: 9781118749838Purchase book