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# Survey of Calculus MATH 2043

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This 4 page Class Notes was uploaded by Silas Langosh on Thursday October 15, 2015. The Class Notes belongs to MATH 2043 at NorthWest Arkansas Community College taught by Staff in Fall. Since its upload, it has received 37 views. For similar materials see /class/224065/math-2043-northwest-arkansas-community-college in Mathematics (M) at NorthWest Arkansas Community College.

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Date Created: 10/15/15

NorthWest Arkansas Community College Fall 2006 Division of Science and quot quot Course Outline Course Math 2043 Survey of Calculus Catalog Description A survey and applications course in calculus designed for students in business life sciences and social sciences Topics include a brief algebra review differentiation curve sketching exponential and logarithmic functions with applications integration and when time permits multivariable calculus Prerequisite Math 1204 with grade of C or better or 24 on Math portion of the ACT or 46 7 100 on the College Algebra portion of the Compass CreditContactLoad hours 3 credit hours 3 contact hours 3 load hours Target Audience and Transfer This course is targeted primarily to students in business and life or social sciences It is required of some AAS and AS degrees as well as a variety of fouryear programs It transfers as 3 credit hours of business calculus General Course Objectives Upon successful completion of this course students should exhibit mastery of certain knowledge and basic skills These topics will include but not be limited to 1 Algebraically and graphically evaluate limits 2 Find basic derivatives using the definition product quotient and chain rules 3 Understand and be able to apply derivatives appropriately to realworld problems to optimize functions find instantaneous rates of change marginal cost marginal profit etc 4 Graph functions by hand including manually finding the extrema using the first derivative test intervals where the graph is increasing and decreasing and finding points of in ection 5 Integrate basic integrals including polynomial functions natural exponential functions and basic u substitutions 6 Relative rates and elasticity of demand 7 Areas between curves 8 Be able to apply integrals appropriately to find the average value accumulated value GTNT index consumer s surplus and producer s surplus 10 Partial Derivatives 11 Optimize functions of several variables including constrained optimization and Lagrange Multipliers Required Text Brief Applied Calculus 4th Edition Berresford Rockett Houghton Mifflin 2007 Required Content Section Top39c 21 Limits and Continuity 22 Slopes Rates of Change and Derivatives 23 Some Differentiation Formulas 24 The Product and Quotient Rules 25 HigherOrder Derivatives 26 The Chain Rule and the Generalized Power Rule 27 Nondifferentiable Functions 31 Graphing Using the First Derivative 32 Graphing Using the First and Second Derivatives 33 Optimization 34 Further Application of Optimization 36 Implicit Differentiation and Related Rates 41 Exponential Functions 42 Logarithmic Function 43 Differentiation of Logarithmic and Exponential Functions Two Applications to Economics Relative Rates and Elasticity of Demand Antiderivatives and Indefinite Integrals Integrations Using Logarithmic and Exponential Functions Definite Integrals and Areas Further Applications of Definite Integrals Average Value and Area Between Curves Two Applications to Economics Consumers Surplus and Income Distribution Integration by Substitution Functions of Several Variables Partial Derivatives Optimizing Functions of Several Variables Lagrange Multipliers and Constrained Optimization Note A variety of application problems from each required topic should be assigned Optiona 11 12 Require Require Instruct Student 1 Sections 13 14 35 61 62 63 64 65 65 74 76 77 d Instructional Activities The content of the course should be taught with graphing calculators as an available tool when appropriate d Forms of Assessment Each instructor must include a set of 9 departmental final exam questions on his or her final exam These questions will be in direct support of the specific objectives stated in the Core Course Objectives will be based on material covered in the Required Text Coverage section and be similar to the questions on the Departmental Review Sheet for Survey of Calculus These questions should be evenly weighted on the final and should compose at least 15 of the students overall grade in the course The questions will be graded using a departmental grading rubric utilizing a 10point scale per question The results of these questions and overall student performance will be reported when final grades are turned in Please note that the only resource other than a graphing calculator allowed for use by students during the nal exam will be a departmental formula sheet for survey of calculus It is also a departmental policy that no TI89 or TI92 or comparable calculators be allowed for use during the nal exam or Resources 1 Instructor s Solutions Manual 2 Printed Test Bank 3 Computerized Test Generator Resources 1 Free tutoring at the Math Cafe and the Learning Lab 2 Student Solutions Manual 3 Sm arthinkingiLive online tutoring 4 Companion Website for students at mathcollegehmcocomstudents 5 Videos available through the NWACC library NorthWest Arkansas Community College Fall 2005 Division of Science and quot quot Course Outline Course Math 2043 Survey of Calculus Catalog Description A survey and applications course in calculus designed for students in business life sciences and social sciences Topics include a brief algebra review differentiation curve sketching exponential and logarithmic functions with applications integration and when time permits multivariable calculus Prerequisite Math 1204 with grade of C or better or 24 on Math portion of the ACT or 46 7 100 on the College Algebra portion of the Compass CreditContactLoad hours 3 credit hours 3 contact hours 3 load hours Target Audience and Transfer This course is targeted primarily to students in business and life or social sciences It is required of some AAS and AS degrees as well as a variety of fouryear programs It transfers as 3 credit hours of business calculus General Course Objectives Upon successful completion of this course students should exhibit mastery of certain knowledge and basic skills These topics will include but not be limited to 1 Algebraically and graphically evaluate limits 2 Find basic derivatives using the definition product quotient and chain rules 3 Understand and be able to apply derivatives appropriately to realworld problems to optimize functions find instantaneous rates of change marginal cost marginal profit etc 4 Graph functions by hand including manually finding the extrema using the first derivative test intervals where the graph is increasing and decreasing and finding points of in ection 5 Integrate basic integrals including polynomial functions natural exponential functions and basic u substitutions 6 Relative rates and elasticity of demand 7 Areas between curves 8 Be able to apply integrals appropriately to find the average value accumulated value consumer s surplus and producer s surplus 9 Partial Derivatives 10 Optimize functions of several variables including constrained optimization and Lagrange Multipliers Required Text Brief Applied Calculus 3rd Edition Berresford Rockett Houghton Mifflin 2004 Required Content Section Top39c 21 Limits and Continuity 22 Slopes Rates of Change and Derivatives 23 Some Differentiation Formulas 24 The Product and Quotient Rules 25 HigherOrder Derivatives 26 The Chain Rule and the Generalized Power Rule 27 Nondifferentiable Functions 31 Graphing Using the First Derivative 32 Graphing Using the First and Second Derivatives 33 Optimization 34 Further Application of Optimization 36 Implicit Differentiation and Related Rates 4 1 Exponential Functions 42 Logarithmic Function 43 Differentiation of Logarithmic and Exponential Functions 44 Two Applications to Economics Relative Rates and Elasticity of Demand 51 Antiderivatives and Indefinite Integrals 52 Integrations Using Logarithmic and Exponential Functions 53 Definite Integrals and Areas 54 Further Applications of Definite Integrals Average Value and Area Between Curves 55 Two Applications to Economics Consumers Surplus and Income Distribution 56 Integration by Substitution 71 Functions of Several Variables 72 Partial Derivatives 73 Optimizing Functions of Several Variables 75 Lagrange Multipliers and Constrained Optimization Note A variety of application problems from each required topic should be assigned Optional Sections 11 12 13 14 35 61 62 63 64 65 65 74 76 77 Required Instructional Activities The content of the course should be taught with graphing calculators as an available tool when appropriate Required Forms of Assessment Each instructor must include a set of 9 departmental final exam questions on his or her final exam These questions will be in direct support of the specific objectives stated in the Core Course Objectives will be based on material covered in the Required Text Coverage section and be similar to the questions on the Departmental Review Sheet for Survey of Calculus These questions should be evenly weighted on the final and should compose at least 15 of the students overall grade in the course The questions will be graded using a departmental grading rubric utilizing a 10point scale per question The results of these questions and overall student performance will be reported when final grades are turned in Please note that the only resource other than a graphing calculator allowed for use by students during the nal exam will be a departmental formula sheet for survey of calculus It is also a departmental policy that no TI89 or TI92 or comparable calculators be allowed for use during the nal exam Instructor Resources 1 Instructor s Solutions Manual 2 Printed Test Bank 3 Computerized Test Generator Student Resources 1 Free tutoring at the Math Cafe and the Learning Lab 2 Student Solutions Manual 3 SmarthinkingiLive online tutoring 4 Companion Website for students at mathcollege hmcocomstudents 5 Videos available through the NWACC library

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