Techniques of Calculus, I Credit: Image adapted from a figure in Applied Calculus: Principles and Applications by Robert Gibbes Thomas, public domain Resource Description A Jupyter notebook companion for a first course in Calculus, including a review of Precalculus concepts. Course Number MATH 110 License MIT Resource Author(s) Table of Contents Online ResourceView the entire resource online here: Techniques of Calculus, I Download Source FilesDownload the resource's source files here: .zip (3.69 MB) Jan Reimann Associate ProfessorDepartment of MathematicsPenn State University318B McAllisterUniversity Park, PA 16802Email: jan.reimann@psu.edu Learn more Precalculus ReviewAlgebraic Simplification TechniquesFactoring TechniquesSolving EquationsGraphingSolving InequalitiesThe Domain of a FunctionTry It YourselfFunctionsFunctions, Domain, and RangeComposition of FunctionsCost, Revenue, and ProfitPower, Polynomial and Rational FunctionsDemand and SupplyAn ApplicationTry It YourselfLimits and ContinuityLimit of a FunctionProperties of Finite LimitsExamples: Computing Limits from GraphsExamples: Computing Limits AlgebraicallyIndeterminate FormsLimits at InfinityContinuityTry It YourselfDerivativesThe Concept of the DerivativeBasic Rules of DifferentiationTry It YourselfMarginal AnalysisCost, Revenue, and ProfitMarginal AnalysisElasticity of DemandElasticity & Total RevenueTry It YourselfImplicit DifferentiationImplicit DifferentiationRelated RatesTry It YourselfCurve SketchingIntervals of Increase and DecreaseRelative ExtremaCritical PointsThe First Derivative TestThe Second Derivative TestIntervals of ConcavityInflection PointsAsymptotesCurve SketchingTry It YourselfOptimizationRelative ExtremaCritical PointsThe First Derivative TestThe Second Derivative TestAbsolute ExtremaApplicationsTry It YourselfExponential and Logarithmic FunctionsExponential and Logarithmic FunctionsLaws of Exponential and Logarithmic FunctionsLogarithmic DifferentiationTry It YourselfCompound InterestNotation and TerminologyAccumulated Amount ExamplesPresent Value ExamplesTry It YourselfIndefinite IntegralsIndefinite IntegralsBasic Rules of IntegrationInitial Value ProblemIntegration by SubstitutionTry It YourselfDefinite IntegralsRiemann Sums and the Definite IntegralThe Fundamental Theorem of CalculusSubstitution for Definite IntegralsAverage Value of a FunctionTry It YourselfApplications of Definite IntegralsArea Between Two CurvesConsumer, Producer, and Total SurplusIncome Streams and AnnuitiesIntegration by Parts and Improper IntegralsIntegration by PartsApplication of Integration by PartsImproper IntegralsApplication of Improper Integrals Keywords / Topics mathematics calculus algebra functions limits continuity differentiation marginal analysis implicit differentiation curve sketching optimization compound interest integration indefinite integrals definite integrals improper integrals integration by parts