Counterexamples: from elementary calculus to the beginnings of analysis

IntroductionCommentsOn the structure of this bookOn mathematical language and notationBackground (elements of theory)SetsFunctionsFUNCTIONS OF ONE REAL VARIABLEElementary properties of functionsElements of theoryFunction definitionBoundednessPeriodicityEven/odd functionsMonotonicityExtremaExercisesLimitsElements of theoryConceptsElementary properties (arithmetic and comparative)ExercisesContinuityElements of theoryLocal propertiesGlobal properties: general resultsGlobal properties: the famous theorems Mapping setsWeierstrass theoremsIntermediate Value theoremUniform continuityExercisesDifferentiationElements of theoryConceptsLocal propertiesGlobal propertiesApplicationsTangent lineMonotonicity and local extremaConvexity and inflectionAsymptotesL'Hospital's ruleExercisesIntegralsElements of theoryIndefinite integralDefinite (Riemann) integralImproper integralsApplicationsExercisesSequences and seriesElements of theoryNumerical sequencesNumerical series: convergence and elementary propertiesNumerical series: convergence testsPower seriesExercisesFUNCTIONS OF TWO REAL VARIABLESLimits and continuityElements of theoryOne-dimensional linksConcepts and local propertiesGlobal propertiesMultidimensional essentialsExercisesDifferentiabilityElements of TheoryOne-dimensional linksConcepts and local propertiesGlobal properties and applicationsMultidimensional essentialsExercisesIntegrabilityElements of theoryOne-dimensional linksMultidimensional essentialsExercisesBibliographySymbol DescriptionIndex.