Advanced Engineering Mathematics with MATLAB

4. New Auflage 2016
ISBN: 978-1-4987-3964-1
Verlag: Taylor & Francis Inc

Buch, Englisch, 1004 Seiten, Format (B × H): 187 mm x 263 mm, Gewicht: 2046 g

Reihe: Advances in Applied Mathematics

Advanced Engineering Mathematics with MATLAB, Fourth Edition builds upon three successful previous editions. It is written for today’s STEM (science, technology, engineering, and mathematics) student.
Three assumptions under lie its structure: (1) All students need a firm grasp of the traditional disciplines of ordinary and partial differential equations, vector calculus and linear algebra. (2) The modern student must have a strong foundation in transform methods because they provide the mathematical basis for electrical and communication studies. (3) The biological revolution requires an understanding of stochastic (random) processes. The chapter on Complex Variables, positioned as the first chapter in previous editions, is now moved to Chapter 10.
The author employs MATLAB to reinforce concepts and solve problems that require heavy computation. Along with several updates and changes from the third edition, the text continues to evolve to meet the needs of today’s instructors and students.
Features:

Complex Variables, formerly Chapter 1, is now Chapter 10.

A new Chapter 18: Itô’s Stochastic Calculus.

Implements numerical methods using MATLAB, updated and expanded

Takes into account the increasing use of probabilistic methods in engineering and the physical sciences

Includes many updated examples, exercises, and projects drawn from the scientific and engineering literature

Draws on the author’s many years of experience as a practitioner and instructor

Gives answers to odd-numbered problems in the back of the book

Offers downloadable MATLAB code at www.crcpress.com

Zielgruppe

This book is intended for instructors and students in the undergraduate advanced engineering mathematics course taught at most four year (engineering) schools in the US and the world. It also could be used in engineering mathematics courses taught in engineering departments. Additionally, it would be beneficial to engineering students looking for an all-in-one mathematics reference.

Autoren/Hrsg.

Duffy, Dean G.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

CLASSIC ENGINEERING MATHEMATICS

First-Order Ordinary Differential EquationsClassification of Differential EquationsSeparation of VariablesHomogeneous EquationsExact EquationsLinear EquationsGraphical SolutionsNumerical Methods
Higher-Order Ordinary Differential EquationsHomogeneous Linear Equations with Constant CoefficientsSimple Harmonic MotionDamped Harmonic MotionMethod of Undetermined CoefficientsForced Harmonic MotionVariation of ParametersEuler-Cauchy EquationPhase DiagramsNumerical Methods
Linear AlgebraFundamentals of Linear AlgebraDeterminantsCramer’s RuleRow Echelon Form and Gaussian EliminationEigenvalues and EigenvectorsSystems of Linear Differential EquationsMatrix Exponential
Vector CalculusReviewDivergence and CurlLine IntegralsThe Potential FunctionSurface IntegralsGreen’s LemmaStokes’ TheoremDivergence Theorem
Fourier SeriesFourier SeriesProperties of Fourier SeriesHalf-Range ExpansionsFourier Series with Phase AnglesComplex Fourier SeriesThe Use of Fourier Series in the Solution of Ordinary Differential EquationsFinite Fourier Series
The Sturm-Liouville ProblemEigenvalues and EigenfunctionsOrthogonality of EigenfunctionsExpansion in Series of EigenfunctionsA Singular Sturm-Liouville Problem: Legendre’s EquationAnother Singular Sturm-Liouville Problem: Bessel’s EquationFinite Element Method
The Wave EquationThe Vibrating StringInitial Conditions: Cauchy ProblemSeparation of VariablesD’Alembert’s FormulaNumerical Solution of the Wave Equation
The Heat EquationDerivation of the Heat EquationInitial and Boundary ConditionsSeparation of VariablesNumerical Solution of the Heat Equation
Laplace’s EquationDerivation of Laplace’s EquationBoundary ConditionsSeparation of VariablesPoisson’s Equation on a RectangleNumerical Solution of Laplace’s EquationFinite Element Solution of Laplace’s Equation
TRANSFORM METHODS
Complex VariablesComplex NumbersFinding RootsThe Derivative in the Complex Plane: The Cauchy-Riemann EquationsLine IntegralsThe Cauchy-Goursat TheoremCauchy’s Integral FormulaTaylor and Laurent Expansions and SingularitiesTheory of ResiduesEvaluation of Real Definite IntegralsCauchy’s Principal Value IntegralConformal Mapping
The Fourier TransformFourier TransformsFourier Transforms Containing the Delta FunctionProperties of Fourier TransformsInversion of Fourier TransformsConvolutionSolution of Ordinary Differential EquationsThe Solution of Laplace’s Equation on the Upper Half-PlaneThe Solution of the Heat Equation
The Laplace TransformDefinition and Elementary PropertiesThe Heaviside Step and Dirac Delta FunctionsSome Useful TheoremsThe Laplace Transform of a Periodic FunctionInversion by Partial Fractions: Heaviside’s Expansion TheoremConvolutionIntegral EquationsSolution of Linear Differential Equations with Constant CoefficientsInversion by Contour IntegrationThe Solution of the Wave EquationThe Solution of the Heat EquationThe Superposition Integral and the Heat EquationThe Solution of Laplace’s Equation
The Z-TransformThe Relationship of the Z-Transform to the Laplace TransformSome Useful PropertiesInverse Z-TransformsSolution of Difference EquationsStability of Discrete-Time Systems
The Hilbert TransformDefinitionSome Useful PropertiesAnalytic SignalsCausality: The Kramers-Kronig Relationship
Green’s FunctionsWhat Is a Green’s Function?Ordinary Differential EquationsJoint Transform MethodWave EquationHeat EquationHelmholtz’s EquationGalerkin Methods
STOCHASTIC PROCESSES
ProbabilityReview of Set TheoryClassic ProbabilityDiscrete Random VariablesContinuous Random VariablesMean and VarianceSome Commonly Used DistributionsJoint Distributions
Random ProcessesFundamental ConceptsPower SpectrumTwo-State Markov ChainsBirth and Death ProcessesPoisson Processes
Itˆo’s Stochastic CalculusRandom Differential EquationsRandom Walk and Brownian MotionItˆo’s Stochastic IntegralItˆo’s LemmaStochastic Differential EquationsNumerical Solution of Stochastic Differential Equations

Über Autor(innen)

Dean G. Duffy is a former mathematics instructor at the US Naval Academy and US Military Academy. He spent 25 years working on numerical weather prediction, oceanic wave modeling, and dynamical meteorology at NASA’s Goddard Space Flight Center. Prior to this, he was a numerical weather prediction officer in the US Air Force. He earned his Ph.D. in meteorology from MIT. Dr. Duffy has written several books on transform methods, engineering mathematics, Green’s functions, and mixed boundary value problems.