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LSU College Readiness Program COURSE PROFILECOURSE NAMELSU Math 1431 Business Calculus (1 semester)COMMON COURSE NUMBERCMAT 2103 Applied CalculusPRIMARY ONLINE CONTENT SOURCECalculus for Business, Economics, Life, and Social Sciences, 12e, MyMathLabBarnett, Ziegler, ByleenCOURSE/UNIT CREDIT? Carnegie UnitGRADE(S)11 or 12PREREQUISITE(S)Math 1021 or MACT min 25CHAPTERS 1 – Linear Equations and Graphs5 – Graphing and Optimization2 – Functions and Graphs6 – Integration3 – Limits and the Derivative7 – Additional Integration4 – Additional Derivative TopicsSECTION NAMES (NUMBER OF EXERCISES) AND LEARNING OBJECTIVESCHAPTER 1: Linear Equations and Graphs1.2 Graphs and Lines (29)Determine whether the slope of a line is positive, negative, zero, or undefinedGraph equationsRecognize the placement of slope and y-intercept in the slope-intercept form of a lineUse the graph of a line to write its equationFind the slope of an equation written in standard formFind the x- and y-intercepts of the graph of a lineWrite equations for vertical and horizontal linesWrite the equation of a line given the slope and a pointWrite the equation of a line given two pointsSolve applicationsCHAPTER 2: Functions and Graphs2.1 Functions (19)Use points on a graph to identify input and output valuesEvaluate functionsFind the domain of a functionSolve applications2.5 Exponential Functions (12)Graph exponential functionsUse properties of exponential functions to solve equationsSolve equations involving exponentialsSolve applicationsCHAPTER 3: Limits and the Derivative3.1 Introduction to Limits (26)Use the graph of a function to estimate limits and function valuesUse the properties of limits to find limits algebraicallySketch the graph of a function using limits and function valuesFind the limit of a difference quotientSolve application problems3.2 Infinite Limits and Limits at Infinity (32)Find infinite limits and limits at infinity using a graphFind limits of rational functionsFind limits of functions at infinityDescribe the behavior of a rational functionFind horizontal and vertical asymptotesEvaluate limits using properties of limitsSolve application problems3.3 Continuity (19)Sketch the graph of a function using limits and function valuesUse the definition of continuityUse continuity properties of functionsUse continuity properties to solve inequalitiesSolve application problems3.4 The Derivative (18)Find average and instantaneous rates of changeUse the four-step process to find the derivative of a functionFind average and instantaneous velocitiesFind the slopes of secant and tangent linesDetermine where a function is differentiable or nondifferentiableSolve application problems3.5 Basic Differentiation Property (34)Use basic differentiation propertiesDifferentiate a constant or a constant times a functionFind slopes of tangent linesFind slopes of tangent lines and values of x where the tangent line is horizontalSolve application problems3.7 Marginal Analysis (14)Find marginal cost, revenue, and profit functionsSolve application problemsCHAPTER 4: Additional Derivative Topics4.1 Continuous Compound Interest (14)Solve equations and evaluate expressions with the constant eGraph equations with continuous compoundingSolve applicationsDetermine the future value of a lump sum of moneySolve continuous compounding problemsSolve applied problems involving compound interestDetermine the present value of a lump sum of money4.2 Derivatives of Exponential and Logarithmic Functions (14)Find derivatives involving exponential and logarithmic functionsFind equations of lines tangent to graphs at particular valuesSolve application problems4.3 Derivatives of Products and Quotients (32)Find derivatives of productsDifferentiate using the product ruleUse the product ruleFind derivatives of quotientsUse the quotient ruleSolve application problems4.4 The Chain Rule (32)Work with composite functionsUse the general power rule to find derivativesUse the chain rule to find derivativesSolve application problems4.7 Elasticity of Demand (9)Find the elasticity of demandDetermine whether demand is elastic, inelastic, or has unit elasticityFind values for which demand is elastic and inelasticSolve application problemsCHAPTER 5: Graphing and Optimization5.1 First Derivatives and Graphs (30)Find intervals on which functions are increasing and decreasingFind local extremaCreate sign charts for graphs of functionsFind critical values of functionsSketch graphs of functionsSolve application problems5.2 Second Derivatives and Graphs (21)Identify particular intervals of graphs of functionsFind inflection pointsGraph function given descriptionsFind inflection points and determine concavity algebraicallyUse curve sketching techniquesSolve application problems5.5 Absolute Maxima and Minima (18)Find absolute extrema of a function5.6a Optimization, Geometric Applications (11)Optimize the product of two numbersSolve area and perimeter optimization problemsSolve construction cost optimization problemsSolve geometric optimization problems5.6b Optimization, Business Applications (10)Solve maximizing revenue and profit problemsSolve inventory control optimization problemsCHAPTER 6: Integration6.1 Antiderivatives and Indefinite Integral (30)Identify antiderivatives and indefinite integralsFind particular antiderivativesSolve application problems6.2 Integration by Substitution (20)Reverse the chain rule to find indefinite integralsUse the method of substitution to find antiderivatives and indefinite integralsSolve application problems6.4 The Definite Integral (14)Identify rectangles under curvesGraph and identify areas by left and right sumsCalculate Riemann sumsUse properties of the definite integral6.5a Fundamental Theorem of Calculus, Basic (20)Compare changes in a function with the area under the graph of the function's derivativeUse the Fundamental Theorem of Calculus to calculate the definite integral of a functionSolve application problemsDetermine the average value of functionsFind average values of functions over intervals6.5b Fundamental Theorem of Calculus, Substitution (13)Evaluate integrals using the Fundamental Theorem of CalculusEvaluate definite integralsEvaluate integrals using substitutionSolve application problemsCHAPTER 7: Additional Integration7.1 Area between Curves (23)Set up a definite integral to represent a shaded areaFind the area between two curvesFind the area under the graphs of nonnegative functions over closed intervals7.2 Applications (13)Solve continuous income stream problemsFind the future value of a continuous income streamSolve consumers' and producers' surplus problemsFind equilibrium points, the consumer surplus, and the producer surplus ................
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