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Advanced Engineering Mathematics with MATLAB 5th Edition by Dean G. Duffy

Advanced Engineering Mathematics with MATLAB 5th Edition by Dean G. Duffy, ISBN-13: 978-0367624057

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Advanced Engineering Mathematics with MATLAB 5th Edition by Dean G. Duffy, ISBN-13: 978-0367624057

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  • Publisher: ‎ Chapman and Hall/CRC; 5th edition (December 31, 2021)
  • Language: ‎ English
  • ‎616 pages
  • ISBN-10: ‎ 0367624052
  • ISBN-13: ‎ 978-0367624057

In the four previous editions the author presented a text firmly grounded in the mathematics that engineers and scientists must understand and know how to use. Tapping into decades of teaching at the US Navy Academy and the US Military Academy and serving for twenty-five years at (NASA) Goddard Space Flight, he combines a teaching and practical experience that is rare among authors of advanced engineering mathematics books.

This edition offers a smaller, easier to read, and useful version of this classic textbook. While competing textbooks continue to grow, the book presents a slimmer, more concise option. Instructors and students alike are rejecting the encyclopedic tome with its higher and higher price aimed at undergraduates.

To assist in the choice of topics included in this new edition, the author reviewed the syllabi of various engineering mathematics courses that are taught at a wide variety of schools. Due to time constraints an instructor can select perhaps three to four topics from the book, the most likely being ordinary differential equations, Laplace transforms, Fourier series and separation of variables to solve the wave, heat, or Laplace’s equation. Laplace transforms are occasionally replaced by linear algebra or vector calculus.

Sturm-Liouville problem and special functions (Legendre and Bessel functions) are included for completeness. Topics such as z-transforms and complex variables are now offered in a companion book, Advanced Engineering Mathematics: A Second Course by the same author.

MATLAB is still employed to reinforce the concepts that are taught. Of course, this Edition continues to offer a wealth of examples and applications from the scientific and engineering literature, a highlight of previous editions. Worked solutions are given in the back of the book.

Table of Contents:

Dedication
v
Contents
vii
Acknowledgments
xiii
Author
xv
Introduction
xvii
ListofDefinitions
xix
Chapter1:
First-OrderOrdinary
DifferentialEquations
1
1.1ClassificationofDifferentialEquations
1
1.2SeparationofVariables
4
1.3HomogeneousEquations
16
1.4ExactEquations
17
1.5LinearEquations
20
vii
1.6GraphicalSolutions
31
1.7NumericalMethods
34
Chapter2:
Higher-OrderOrdinary
Differential Equations
47
2.1HomogeneousLinearEquationswithConstantCoefficients
51
2.2SimpleHarmonicMotion
59
2.3DampedHarmonicMotion
63
2.4MethodofUndeterminedCoefficients
68
2.5ForcedHarmonicMotion
73
2.6VariationofParameters
80
2.7Euler-CauchyEquation
85
2.8PhaseDiagrams
88
2.9NumericalMethods
93
Chapter3:Linear Algebra
101
3.1Fundamentals
101
3.2Determinants
109
3.3Cramer’sRule
113
3.4RowEchelonFormandGaussianElimination
115
3.5EigenvaluesandEigenvectors
129
3.6SystemsofLinearDifferentialEquations
136
3.7MatrixExponential
141
TableofContents ix
Chapter4:VectorCalculus1474.1Review1474.2DivergenceandCurl1544.3LineIntegrals1584.4ThePotentialFunction1634.5SurfaceIntegrals1644.6Green’sLemma1714.7Stokes’Theorem1744.8DivergenceTheorem181Chapter5:FourierSeries1895.1FourierSeries1905.2PropertiesofFourierSeries2025.3Half-RangeExpansions2115.4FourierSerieswithPhaseAngles2165.5ComplexFourierSeries2205.6TheUseofFourierSeriesintheSolutionofOrdinaryDifferentialEquations2255.7FiniteFourierSeries232Chapter6:TheFourierTransform2496.1FourierTransforms2496.2FourierTransformsContainingtheDeltaFunction262
6.3
PropertiesofFourierTransforms
264
6.4
InversionofFourierTransforms
275
6.5
Convolution
279
6.6
TheSolutionofOrdinaryDifferentialEquationsbyFourierTransforms
283
6.7
TheSolutionofLaplace’sEquationontheUpperHalf-Plane
285
6.8
TheSolutionoftheHeatEquation
287
Chapter7:
TheLaplaceTransform
295
7.1
DefinitionandElementaryProperties
295
7.2
TheHeavisideStepandDiracDeltaFunctions
299
7.3
SomeUsefulTheorems
307
7.4
TheLaplaceTransformofaPeriodicFunction
315
7.5
InversionbyPartialFractions:Heaviside’sExpansionTheorem
317
7.6
Convolution
324
7.7
SolutionofLinearDifferentialEquationswithConstantCoefficients
329
Chapter8:
TheWaveEquation
347
8.1
TheVibratingString
348
8.2
InitialConditions:CauchyProblem
351
8.3
SeparationofVariables
351
8.4
D’Alembert’sFormula
365
8.5
NumericalSolutionoftheWaveEquation
372
Chapter9:TheHeatEquation3879.1DerivationoftheHeatEquation3879.2InitialandBoundaryConditions3899.3SeparationofVariables3909.4TheSuperpositionIntegral4059.5NumericalSolutionoftheHeatEquation409
Chapter10:Laplace’sEquation41910.1DerivationofLaplace’sEquation41910.2BoundaryConditions42110.3SeparationofVariables42210.4Poisson’sEquationonaRectangle42910.5NumericalSolutionofLaplace’sEquation433
Chapter11:TheSturm-LiouvilleProblem44311.1EigenvaluesandEigenfunctions44411.2OrthogonalityofEigenfunctions45711.3ExpansioninSeriesofEigenfunctions46111.4FiniteElementMethod485
Chapter12:
SpecialFunctions493
12.1LegendrePolynomials495
12.2BesselFunctions519
12.AAppendixA:DerivationoftheLaplacianinPolarCoordinates567
12.BAppendixB:DerivationoftheLaplacianinSphericalPolarCoordinates568
AnswerstotheOdd-NumberedProblems571
Index589

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, and mixed boundary value problems including Green’s Functions with Applications, Second Edition, published by CRC Press.

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