Includes bibliographical references and index.

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.