MARC record from Internet Archive

LEADER: 08866cam 2200865 a 4500
001 ocn122314994
003 OCoLC
005 20220730091640.0
008 061005s2007 caua ob 000 0 eng d
006 m o d
007 cr |n|---|||||
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020 $a1598291874$q(ebook)
020 $a9781598291872$q(ebook)
020 $z1598291866$q(pbk.)
020 $z9781598291865$q(pbk.)
020 $z9781188294446
024 7 $a10.2200/S00082ED1V01Y200612ENG003$2doi
035 $a(OCoLC)122314994$z(OCoLC)456124471$z(OCoLC)785733518$z(OCoLC)785776100$z(OCoLC)958839798$z(OCoLC)987457495$z(OCoLC)1027289136$z(OCoLC)1044368940$z(OCoLC)1058095427$z(OCoLC)1078033526$z(OCoLC)1087005662
050 4 $aQA374$b.W37 2007
055 3 $aTA330$b.W274 2007
072 7 $aTEC$x009000$2bisacsh
072 7 $aTEC$x035000$2bisacsh
082 04 $a620.00151$222
100 1 $aWatts, Robert G.
245 10 $aEssentials of applied mathematics for scientists and engineers /$cRobert G. Watts.
250 $a1st ed.
260 $a[San Rafael, Calif.] :$bMorgan & Claypool Publishers,$c©2007.
300 $a1 online resource (ix, 169 pages)
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
490 1 $aSynthesis lectures on engineering sequence in series,$x1559-8128 ;$v#3
500 $aTitle from PDF title page (viewed March 27, 2007).
504 $aIncludes bibliographical references.
505 0 $aPartial differential equations in engineering -- Introductory comments -- Fundamental concepts -- Problems -- The heat conduction (or diffusion) equation -- Rectangular Cartesian coordinates -- Cylindrical coordinates -- Spherical coordinates -- The Laplacian operator -- Boundary conditions -- The vibrating string -- Boundary conditions -- Vibrating membrane -- Longitudinal displacements of an elastic bar -- Further reading -- The Fourier method: Separation of variables -- Heat conduction -- Scales and dimensionless variables -- Separation of variables -- Superposition -- Orthogonality -- Lessons -- Problems -- Scales and dimensionless variables -- Separation of variables -- Choosing the sign of the separation constant -- Superposition -- Orthogonality -- Lessons -- Scales and dimensionless variables -- Getting to one nonhomogeneous condition -- Separation of variables -- Choosing the sign of the separation constant -- Superposition -- Orthogonality -- Lessons -- Scales and dimensionless variables -- Relocating the nonhomogeneity -- Separating variables -- Superposition -- Orthogonality -- Lessons -- Problems -- Vibrations -- Scales and dimensionless variables -- Separation of variables -- Orthogonality -- Lessons -- Problems -- Further reading -- Orthogonal sets of functions -- Vectors -- Orthogonality of vectors -- Orthonormal sets of vectors -- Functions -- Orthonormal sets of functions and Fourier series -- Best approximation -- Convergence of Fourier series -- Examples of Fourier series -- Problems -- Sturm-Liouville problems: Orthogonal functions -- Orthogonality of Eigenfunctions -- Problems -- Further reading -- Series solutions of ordinary differential equations -- General series solutions -- Definitions -- Ordinary points and series solutions -- Lessons: Finding series solutions for differential equations with ordinary points -- Problems -- Regular singular points and the method of Frobenius -- Lessons: Finding series solution for differential equations with regular singular points -- Logarithms and second solutions -- Problems -- Bessel functions -- Solutions of Bessel's equation -- Here are the rules -- Fourier-Bessel series -- Problems -- Legendre functions -- Associated Legendre functions -- Problems -- Further reading -- Solutions using Fourier series and integrals -- Conduction (or diffusion) problems -- Time-dependent boundary conditions -- Vibrations problems -- Problems -- Fourier integrals -- Problem -- Further reading -- Integral transforms: The Laplace transform -- The Laplace transform -- Some important transforms -- Exponentials -- Shifting in the S-domain -- Shifting in the time domain -- Sine and cosine -- Hyperbolic functions -- Powers of t: tm -- Heaviside step -- The Dirac delta function -- Transforms of derivatives -- Laplace transforms of integrals -- Derivatives of transforms -- Linear ordinary differential equations with constant coefficients -- Some important theorems -- Initial value theorem -- Final value theorem -- Convolution -- Partial fractions -- Nonrepeating roots -- Repeated roots -- Quadratic factors: Complex roots -- Problems -- Further reading -- Complex variables and the Laplace inversion integral -- Basic properties -- Limits and differentiation of complex variables analytic functions -- Integrals -- The Cauchy integral formula -- Problems -- Solutions with Laplace transforms -- Mechanical vibrations -- Problems -- Diffusion or conduction problems -- Problems -- Duhamel's theorem -- Problems -- Further reading -- Sturm-Liouville Transforms -- A Preliminary Example: Fourier Sine Transform -- Generalization: The Sturm-Liouville Transform: Theory -- The Inverse Transform -- Problems -- Further Reading -- Introduction to Perturbation methods -- Examples from algebra -- Regular perturbation -- Singular perturbation -- Appendix A: The roots of certain transcendental equations.
520 $aThis is a book about linear partial differential equations that are common in engineering and the physical sciences. It will be useful to graduate students and advanced undergraduates in all engineering fields as well as students of physics, chemistry, geophysics and other physical sciences and professional engineers who wish to learn about how advanced mathematics can be used in their professions. The reader will learn about applications to heat transfer, fluid flow, mechanical vibrations. The book is written in such a way that solution methods and application to physical problems are emphasized. There are many examples presented in detail and fully explained in their relation to the real world. References to suggested further reading are included. The topics that are covered include classical separation of variables and orthogonal functions, Laplace transforms, complex variables and Sturm-Liouville transforms.
546 $aEnglish.
650 0 $aDifferential equations, Partial$xNumerical solutions.
650 0 $aDifferential equations, Linear$xNumerical solutions.
650 0 $aEngineering mathematics.
650 6 $aÉquations aux dérivées partielles$xSolutions numériques.
650 6 $aÉquations différentielles linéaires$xSolutions numériques.
650 6 $aMathématiques de l'ingénieur.
650 7 $aTECHNOLOGY & ENGINEERING$xEngineering (General)$2bisacsh
650 7 $aTECHNOLOGY & ENGINEERING$xReference.$2bisacsh
650 7 $aDifferential equations, Linear$xNumerical solutions.$2fast$0(OCoLC)fst00893471
650 7 $aDifferential equations, Partial$xNumerical solutions.$2fast$0(OCoLC)fst00893488
650 7 $aEngineering mathematics.$2fast$0(OCoLC)fst00910601
655 4 $aElectronic books.
776 08 $iPrint version:$z9781598291865
830 0 $aSynthesis lectures on engineering (Online) ;$v#3.
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856 40 $3Morgan & Claypool$uhttps://doi.org/10.2200/S00082ED1V01Y200612ENG003
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856 42 $3Morgan & Claypool$uhttp://www.morganclaypool.com/doi/abs/10.2200/S00082ED1V01Y200612ENG003
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