Mathematics for Engineers and Scientists: For Engineers and Scientists

ISBN-13: 9781584884880 / Angielski / Miękka / 2004 / 1010 str.

W. H. C. Bassetti; Alan Jeffrey

Opis

Since its original publication in 1969, Mathematics for Engineers and Scientists has built a solid foundation in mathematics for legions of undergraduate science and engineering students. It continues to do so, but as the influence of computers has grown and syllabi have evolved, once again the time has come for a new edition.
Thoroughly revised to meet the needs of today's curricula, Mathematics for Engineers and Scientists, Sixth Edition covers all of the topics typically introduced to first- or second-year engineering students, from number systems, functions, and vectors to series, differential equations, and numerical analysis. Among the most significant revisions to this edition are:

Simplified presentation of many topics and expanded explanations that further ease the comprehension of incoming engineering students

A new chapter on double integrals

Many more exercises, applications, and worked examples

A new chapter introducing the MATLAB and Maple software packages
Although designed as a textbook with problem sets in each chapter and selected answers at the end of the book, Mathematics for Engineers and Scientists, Sixth Edition serves equally well as a supplemental text and for self-study. The author strongly encourages readers to make use of computer algebra software, to experiment with it, and to learn more about mathematical functions and the operations that it can perform.

Spis treści

NUMBERS, TRIGONOMETRIC FUNCTIONS AND COORDINATE GEOMETRYSets and numbersIntegers, rationals and arithmetic laws Absolute value of a real numberMathematical inductionReview of trigonometric propertiesCartesian geometryPolar coordinatesCompleting the squareLogarithmic functionsGreek symbols used in mathematicsVARIABLES, FUNCTIONS AND MAPPINGSVariables and functionsInverse functionsSome special functionsCurves and parametersFunctions of several real variablesSEQUENCES, LIMITS AND CONTINUITYSequencesLimits of sequencesThe number eLimits of functions -/ continuityFunctions of several variables -/ limits, continuityA useful connecting theoremAsymptotesCOMPLEX NUMBERS AND VECTORSIntroductory ideasBasic algebraic rules for complex numbersComplex numbers as vectorsModulus -/ argument form of complex numbersRoots of complex numbersIntroduction to space vectorsScalar and vector productsGeometrical applicationsApplications to mechanicsProblemsDIFFERENTIATION OF FUNCTIONS OF ONE OR MORE REAL VARIABLESThe derivativeRules of differentiationSome important consequences of differentiabilityHigher derivatives _/ applicationsPartial differentiationTotal differentialsEnvelopesThe chain rule and its consequencesChange of variableSome applications of dy/dx=1/ dx/dyHigher-order partial derivativesEXPONENTIAL, LOGARITHMIC AND HYPERBOLIC FUNCTIONS AND AN INTRODUCTION TO COMPLEX FUNCTIONSThe exponential functionDifferentiation of functions involving the exponential functionThe logarithmic functionHyperbolic functionsExponential function with a complex argumentFunctions of a complex variable, limits, continuity and differentiabilityFUNDAMENTALS OF INTEGRATIONDefinite integrals and areasIntegration of arbitrary continuous functionsIntegral inequalitiesThe definite integral as a function of its upper limit -/ the indefinite integralDifferentiation of an integral containing a parameterOther geometrical applications of definite integralsCentre of mass and moment of inertiaLine integralsSYSTEMATIC INTEGRATIONIntegration of elementary functionsIntegration by substitutionIntegration by partsReduction formulaeIntegration of rational functions - partial fractionsOther special techniques of integrationIntegration by means of tablesProblemsDOUBLE INTEGRALS IN CARTESIAN AND PLANE POLAR COORDINATESDouble integrals in Cartesian coordinatesDouble integrals using polar coordinatesProblemsMATRICES AND LINEAR TRANSFORMATIONSMatrix algebraDeterminantsLinear dependence and linear independenceInverse and adjoint matricesMatrix functions of a single variableSolution of systems of linear equationsEigenvalues and eigenvectorsMatrix interpretation of change of variables in partial differentiationLinear transformationsApplications of matrices and linear transformationsProblemsSCALARS, VECTORS AND FIELDSCurves in spaceAntiderivatives and integrals of vector functionsSome applicationsFields, gradient and directional derivativeDivergence and curl of a vectorConservative fields and potential functionsProblemsSERIES, TAYLOR'S THEOREM AND ITS USESSeriesPower seriesTaylor's theoremApplications of Taylor's theoremApplications of the generalized mean value theoremDIFFERENTIAL EQUATIONS AND GEOMETRYIntroductory ideasPossible physical origin of some equationsArbitrary constants and initial conditionsFirst-order equations - direction fields and isoclinesOrthogonal trajectoriesFirst-order differential equationsEquations with separable variablesHomogeneous equationsExact equationsThe linear equation of first orderDirect deductionsHIGHER-ORDER LINEAR DIFFERENTIAL EQUATIONSLinear equations with constant coefficients _/ homogeneous caseLinear equations with constant coefficients _/ inhomogeneous caseVariation of parametersOscillatory solutionsCoupled oscillations and normal modesSystems of first-order equationsTwo-point boundary value problemsThe Laplace transformThe Delta functionApplications of the Laplace transformFOURIER SERIESIntroductory ideasConvergence of Fourier seriesDifferent forms of Fourier seriesDifferentiation and integrationNUMERICAL ANALYSISErrors and efficient methods of calculationSolution of linear equationsInterpolationNumerical integrationSolution of polynomial and transcendental equationsNumerical solutions of differential equationsDetermination of eigenvalues and eigenvectorsPROBABILITY AND STATISTICSThe elements of set theory for use in probability and statisticsProbability, discrete distributions and momentsContinuous distributions and the normal distributionMean and variance of a sum of random variablesStatistics - inference drawn from observationsLinear regressionSYMBOLIC ALGEBRAIC MANIPULATION BY COMPUTER SOFTWAREMapleMATLABANSWERSREFERENCE LISTS:Useful identities and constantsBasic derivatives and rulesLaplace transform pairsShort table of integralsINDEX

O autorze

Alan Jeffrey