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Business CalculusMath 01204 Credits1. This course is an introduction to calculus for students in business, economics and other social sciences. Application of concepts is stressed throughout the course. 2. A rigorous high school algebra that includes exponentials and logarithmic functions or precalculus is a prerequisite for the course. Proficiency in algebraic manipulation is essential.3. The grade is determined by the student's performance on three exams and a comprehensive final.4. The recommended text for this course is Brief Applied Calculus by Berresford and Rockett, 6th ed. Brooks/Cole, Cengage Learning.The following topics are covered in the University of Pittsburgh Math 0120 course:1. DerivativesLimitsIntroduction to limitsApproaching infinityOne-sided limitsContinuityTangents as rate of changeDefinition of derivativesRules for derivativesPolynomialsProductsQuotientsChain RulePowersImplicit differentiationHigher-order derivativesRelated rates2. Application of the DerivativeGraphing using:First derivativeSecond derivativeAsymptotes andinterceptsAbsolute extrema on agiven domainOptimizing problemsDifferentialsMarginal analysis in business3. Exponential and Logarithmic FunctionsAlgebraic properties reviewGraphs of exponential/log functionsConstant e Compounding InterestDerivativesChain RuleElasticity of Demand4. IntegrationAntiderivatives and Indefinite integralsIntegration rules and proceduresPolynomialsPowersExponentials/logarithmicDefinite integralDefinite integral as a limit of a Riemann sumFundamental theorem of integral calculusArea under the curve and between curvesIntegration by substitutionIntegration by partsIntegration using tablesImproper integralsNumerical IntegrationTrapezoidal and/or Simpson’s RuleApplicationsRecovering cost from marginal costCost of a succession of unitsAverage value of a functionConsumer and producer's surplusDifferential EquationsGeneral and particular solutionsSeparation of variables5. Multivariable calculusFunctions of several variablesPartial derivativesMaxima and minima, the D testLaGrange multipliersOPTIONAL:Method of least squaresDouble integrals over rectangular regionsLogistic GrowthTrigonometric functionsBasic trigonometric values, graphs, and lawsDerivativesIntegralsArithmetic and Geometric Progressions ................
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