Syllabus MATH 1600 Geometry And Calculus I 2021

DocuSign Envelope ID: D72082D0-1A48-481A-BBF3-A84CD7944D17SyllabusMATH 1600Analytic Geometry and Calculus I2021Committee Members:Chin Ng, Central Community CollegeChad Haugen, Metropolitan Community CollegeJoanna Jacobs, Mid‐Plains Community CollegeBeth Welke, Northeast Community CollegeGina Seebohm, Southeast Community CollegeScott Schaub, Western Nebraska Community CollegeJody Wingert, Alyssa Turnquist, Little Priest Tribal CollegeAl Widrowicz, Nebraska Indian Community CollegeFacilitator: Beth WelkeThe Institution agrees to the contents in this syllabus including course prefix, number, course description andother contents of this syllabus.03/30/2021Chief Academic Officer, Central Community CollegeAdopt03/26/2021Chief Academic Officer, Little Priest Tribal CollegeAdopt03/29/2021Chief Academic Officer, Metropolitan Community CollegeDecline03/26/2021Chief Academic Officer, Mid‐Plains Community CollegeAdopt03/27/2021Chief Academic Officer, Nebraska Indian Community CollegeAdopt03/26/2021Chief Academic Officer, Northeast Community CollegeAdopt03/29/2021Chief Academic Officer, Southeast Community CollegeAdopt03/30/2021Chief Academic Officer, Western Nebraska Community CollegeAdopt

DocuSign Envelope ID: D72082D0-1A48-481A-BBF3-A84CD7944D17I.CATALOG DESCRIPTIONMATH 1600Analytic Geometry and Calculus IPrerequisite: College Algebra & Trigonometry or PreCalculus or appropriate placementscore.This course is a study of analytical geometry and single variable calculus. Topics includelimits, continuity, derivatives, applications of derivatives, integrals, and applications ofintegrals.5.0 semester credit hours/ 7.5 quarter credit hours/75 contact hoursII.COURSE OBJECTIVES/COMPETENCIESThe course will:1.2.3.4.5.Present analytical, numerical and graphical techniques to establish limits.Introduce analytical, numerical and graphical techniques to verify continuity.Present the definition to find derivatives.Provide the rules of differentiation to calculate derivatives.Relate the concepts of differentiation to analyze increasing and decreasing functions,locate extrema and determine concavity.6. Use the concepts of differentiation to calculate rates of change.7. Present model functions and use techniques of differentiation to optimize thefunction.8. Use the definition of integrals and approximation.9. Provide the rules of integration to calculate integrals.10. Relate the concepts of integration to calculate area between curves.11. Use the concepts of integration to calculate volumes of solids.Nebraska Transfer InitiativeMATH1600 – Analytic Geometry and Calculus IUpdated: 2021Page 1 of 5

DocuSign Envelope ID: D72082D0-1A48-481A-BBF3-A84CD7944D17III.STUDENT LEARNING OUTCOMESLimits and ContinuityOutcomes: Students will be able to: Evaluate rates of changeFind the equation of a tangent to a curveCalculate limits of a function using the limit lawsEvaluate one-sided limits and limits at infinityEvaluate infinite limits and find vertical asymptotesVerify continuity of functionsDerivativesOutcomes: Students will be able to: Find derivatives and equations of tangents at a pointExpress the derivative as a functionUtilize differentiation rules for polynomials, products, and quotientsInterpret the derivative as a rate of changeFind the derivatives of transcendental functionsUtilize the chain ruleDetermine higher order derivativesUse implicit differentiationUtilize the mean value theoremApplications of DerivativesOutcomes: Students will be able to: Determine absolute extremaSolve related rates problemsUtilize linearization and differentialsUse the first and second derivatives to identify local extrema and sketch curvesSolve applied optimization problemsUtilize Newton’s MethodNebraska Transfer InitiativeMATH1600 – Analytic Geometry and Calculus IUpdated: 2021Page 2 of 5

DocuSign Envelope ID: mes: Students will be able to: Estimate with finite sumsUse sigma notation and limits of finite sumsEvaluate definite integralsUtilize the fundamental theorem of calculusEvaluate indefinite integralsUse the substitution method to evaluate integralsFind the area under a curve and between curvesApplications of Definite IntegralsOutcomes: Students will be able to: Determine volumes by slicing and rotation about an axis Evaluate volumes by cylindrical shellsIV.CONTENT/TOPICAL OUTLINEA. Limits and Continuity1. Rates of change2. Limits of functions3. ContinuityB. Derivatives1. Derivative at a point2. Derivative as a function3. Differentiation Rules4. Derivative as Rate of Change5. Derivatives of Transcendentals Functions6. Chain Rule7. Implicit Differentiation8. Higher Order Derivatives9. Linearization and DifferentialsNebraska Transfer InitiativeMATH1600 – Analytic Geometry and Calculus IUpdated: 2021Page 3 of 5

DocuSign Envelope ID: D72082D0-1A48-481A-BBF3-A84CD7944D17C. Applications of Derivatives1. Extreme values of functions2. Mean value theorem3. First and Second Derivative Test4. Concavity5. Applied Optimization6. Related Rates7. Newton’s Method8. AntiderivativesD. Integrals1. Finite sums2. Definite integral3. Fundamental Theorem of Calculus4. Indefinite Integrals5. Substitution Method6. Area between curvesE. Applications of Definite Integrals1. Volumes using cross-sections2. Volumes using cylindrical shellsV.INSTRUCTIONAL MATERIALSSUGGESTED TEXTBOOKS and/or MATERIALS1.2.3.4.5.6.Calculus Early Transcendentals; Thomas, PearsonCalculus; Larson & Edwards, CengageUniversity Calculus; Hass, PearsonCalculus; Stewart-Thomson, Brooks/ColeCalculus Early Transcendentals; Briggs/Cochran, PearsonCalculus Volume 1; Herman & Strang, Openstax Rice UniversityEquipment: Graphing calculator recommendedNebraska Transfer InitiativeMATH1600 – Analytic Geometry and Calculus IUpdated: 2021Page 4 of 5

DocuSign Envelope ID: D72082D0-1A48-481A-BBF3-A84CD7944D17VI.METHODS OF PRESENTATION/INSTRUCTIONA. Methods of presentation are determined by the instructor. They traditionallyinclude some combination of the following:1. Lecture2. Class Discussion3. Presentation and discussion of solutions to problems and exercisesVII.METHODS OF EVALUATIONA. Methods of evaluation are determined by the instructor. Evaluation traditionallyinclude some combination of the following:1.2.3.4.Unit TestsComprehensive final examQuizzesAssignmentsB. Students will receive a course outline/syllabus indicating the instructor’s specificattendance policy, course timeline, course requirements, and grading criteria.VIII.INSTITUTIONAL DEFINED SECTION(To be used at the discretion of each community college as deemed necessary)Nebraska Transfer InitiativeMATH1600 – Analytic Geometry and Calculus IUpdated: 2021Page 5 of 5

Nebraska Transfer Initiative MATH1600 – Analytic Geometry and Calculus I Updated: 2021 Page 4 of 5 C. Applications of Derivatives 1. Extreme values of functions 2. Mean value theorem 3. First and Second Derivative Test 4. Concavity 5. Applied Optimization 6. Related Rat