Mathematics for Engineers and Scientists, Sixth Edition

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 -/ l. Read more... Abstract: 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 -/ l 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 Content: Front Cover Contents Preface to the sixth edition Preface to the first edition Supplementary computer problems xv 1. Numbers, trigonometric functions and coordinate geometry 2. Variables, functions and mappings 3. Sequences, limits and continuity 4. Complex numbers and vectors 5 Differentiation of functions of one or more real variables 6. Exponential, logarithmic and hyperbolic functions and an introduction to complex functions 7. Fundamentals of integration 8. Systematic integration 9. Double integrals in Cartesian and plane polar coordinates 10. Matrices and linear transformations11. Scalars, vectors and fields 12. Series, Taylor's theorem and its uses 13. Differential equations and geometry 14. First-order differential equations 15. Higher-order linear differential equations 16. Fourier series 17. Numerical analysis 18. Probability and statistics 19. Symbolic algebraic manipulation by computer software Answers Reference list 1: Useful identities and constants Reference list 2: Basic derivaties and rules Reference list 3: Laplace transform pairs Reference list 4: Short table of integrals Abstract: NUMBERS, TRIGONOMETRIC FUNCTIONS AND COORDINATE GEOMETRY Sets and numbers Integers, rationals and arithmetic laws Absolute value of a real number Mathematical induction Review of trigonometric properties Cartesian geometry Polar coordinates Completing the square Logarithmic functions Greek symbols used in mathematics VARIABLES, FUNCTIONS AND MAPPINGS Variables and functions Inverse functions Some special functions Curves and parameters Functions of several real variables SEQUENCES, LIMITS AND CONTINUITY Sequences Limits of sequences The number e Limits of functions -/ continuity Functions of several variables -/ l "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-year engineering students, from number systems, functions, and vectors to series, differential equations, and numerical analysis." "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."--Jacket 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 rev