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General Information

Course ID (CB01A and CB01B)
MATH D012.
Course Title (CB02)
Introductory Calculus for Business and Social Science
Course Credit Status
Credit - Degree Applicable
Effective Term
Fall 2023
Course Description
This is an introduction to limits, differentiation, and integration of single and multivariate functions, with applications in business, economics, and social sciences.
Faculty Requirements
Course Family
Not Applicable

Course Justification

This course is a major preparation in the discipline of various business-related majors for at least one CSU or UC. This course satisfies the CSU GE/Breadth requirement Area B4 Mathematics and Quantitative Reasoning. This course satisfies the IGETC requirement Area 2 Mathematical Concepts and Quantitative Reasoning. This course satisfies the mathematics proficiency requirement for the Liberal Arts A.A. degree and the Business Administration A.S.-T degree. This course meets the needs of students in business-related majors that require a basic understanding of calculus and its applications to business without having to learn calculus at a more rigorous level.

Foothill Equivalency

Does the course have a Foothill equivalent?
Yes
Foothill Course ID
MATH F012.

Course Philosophy

Formerly Statement

Course Development Options

Basic Skill Status (CB08)
Course is not a basic skills course.
Grade Options
  • Letter Grade
  • Pass/No Pass
Repeat Limit
0

Transferability & Gen. Ed. Options

Transferability
Transferable to both UC and CSU
CSU GEArea(s)StatusDetails
CGB4CSU GE Area B4 - Mathematics/Quantitative ReasoningApproved
IGETCArea(s)StatusDetails
IG2XIGETC Area 2 - Mathematical Concepts and Quantitative ReasoningApproved
C-IDArea(s)StatusDetails
MATHMathematicsApprovedC-ID MATH 140

Units and Hours

Summary

Minimum Credit Units
5.0
Maximum Credit Units
5.0

Weekly Student Hours

TypeIn ClassOut of Class
Lecture Hours5.010.0
Laboratory Hours0.00.0

Course Student Hours

Course Duration (Weeks)
12.0
Hours per unit divisor
36.0
Course In-Class (Contact) Hours
Lecture
60.0
Laboratory
0.0
Total
60.0
Course Out-of-Class Hours
Lecture
120.0
Laboratory
0.0
NA
0.0
Total
120.0

Prerequisite(s)

MATH D031., MATH D031H, MATH D031B, MATH D041. or MATH D041H

Corequisite(s)

Advisory(ies)

ESL D272. and ESL D273., or ESL D472. and ESL D473., or eligibility for EWRT D001A or EWRT D01AH or ESL D005.

Limitation(s) on Enrollment

Entrance Skill(s)

General Course Statement(s)

(See general education pages for the requirements this course meets.)

Methods of Instruction

Lecture and visual aids

Discussion and problem solving performed in class

Quiz and examination review performed in class

Collaborative learning and small group exercises

Assignments

  1. Readings from the text and other (optional) sources
  2. Written assignments which may include
    1. Problem solving exercises from the text that include written explanations of concepts and justification of conclusions.
    2. Problems requiring written explanations of key concepts, analysis of problem solving strategies and use of mathematical vocabulary
    3. Projects may be used to enhance students' understanding of topics studied in the course in group or individual formats, whether communicating their understanding orally through classroom presentation or in writing.

Methods of Evaluation

  1. Problem solving exercises (homework) and/or quizzes which will be evaluated for accuracy and completion in order to assess student’s comprehension of material covered in lecture and to provide feedback to students on their progress. Questions may also require the student to communicate ideas and conclusions in short essay format.
  2. A minimum of three one hour examinations or two one hour exams and a project composed of both computational and concept based questions which will require the student to demonstrate ability in integrating the methods, ideas and techniques learned in class. Questions may also require the student to communicate ideas and conclusions in short essay format.
  3. A two-hour comprehensive final examination composed of both computational and concept based questions which will require the student to demonstrate ability in integrating the methods, ideas and techniques learned in class. Questions may also require the student to communicate ideas and conclusions in short essay format.
  4. Evaluation of projects are to be based on completion and comprehension of course content, and students shall receive timely feedback on their progress.

Essential Student Materials/Essential College Facilities

Essential Student Materials: 
  • Graphing calculator recommended
Essential College Facilities:
  • None.

Examples of Primary Texts and References

AuthorTitlePublisherDate/EditionISBN
Applied Calculus for Business and Economics. By Gerald Beer, Little Brown 1978
Applied Calculus: For Business, Economics, and the Social and Life Sciences, By Laurence D & Gerald L, Bradley Hoffman et.al, 11th Edition, McGraw-Hill publisher, 2012.
Hughes-Hallett et all. "Applied Calculus," 5th ed. John Wiley and Sons, Inc, 2013.
Bittinger, Surgent, and Ellenbogen. "Calculus and Its Applications", 11th ed, Pearson/Addison Wesley, 2014.

Examples of Supporting Texts and References

AuthorTitlePublisher
Joseph, George G., "The Crest of Peacock," 3rd Edition. Princeton University Press, 2010. (Supplement to non-European history of Calculus development)

Learning Outcomes and Objectives

Course Objectives

  • Discuss functions and use them to build mathematical models in the sciences including business and economics
  • Define and discuss limits and study their properties and determine continuity/discontinuities of a function.
  • Apply the definition of derivatives and use both the definition and rules of differentiations to find rates of change and equations of tangent lines.
  • Apply the chain rule to differentiate composite functions, inverse functions and functions defined implicitly.
  • Use Algebra and first and second derivatives to assist in sketching graphs of functions and use derivatives and graphs to analyze functions that model economic and business applications.
  • Apply the first and second derivative tests to solve optimization problems including application in business and economics
  • Examine integration of functions as Riemann sums of products, such as area, and use limits of Riemann sums, antiderivatives, tables, software and numerical techniques to evaluate/approximate definite integrals.
  • Use integrations techniques to solve application problems including first order separable differential equations.
  • Apply rules of partial differentiation to find partial derivatives of of multivariable functions and solve optimization problems including applications in business and economics.
  • Classify improper integrals and examine their properties and use to solve applications problems

CSLOs

  • Use correct notation and mathematical precision in the evaluation and interpretation of derivatives and integrals.

  • Evaluate, solve, interpret and communicate business and social science applications using appropriate differentiation and integration methodologies.

Outline

  1. Discuss functions and use them to build mathematical models in the sciences including business and economics
    1. Find the domain and range of functions
      1. Linear, quadratic and higher degree polynomial functions.
      2. Exponential functions
      3. Logarithmic functions
      4. piecewise defined functions
    2. Use properties of exponents and logarithms to
      1. Simplify exponential and logarithmic expressions
      2. Expand and condense logarithmic expressions
    3. Use functions to find application models such as
      1. Supply and Demand as linear models
      2. Cost-Output models
      3. Revenue and profit as quadratic models
      4. Find equilibrium prices and break even in cost and revenue
  2. Define and discuss limits and study their properties and determine continuity/discontinuities of a function.
    1. Interpret limits of functions at a point:
      1. as a slope of a tangent line
      2. as a rate of change of a function
    2. Use Algebra and properties of limits to evaluate limits
    3. Identify points in the domain of a function where the limit does not exist
    4. Apply definition of continuity to determine the continuity/discontinuity of a function at a point.
  3. Apply the definition of derivatives and use both the definition and rules of differentiations to find rates of change and equations of tangent lines.
    1. Compute derivatives of elementary functions as a limit of a difference quotient.
    2. Interpret the derivative as a slope of a tangent line
      1. Find slopes of tangent lines
      2. Find equations of tangent lines
    3. Compute average and instantaneous rate of change of functions as
      1. Rate of change of the value of an annuity
      2. Elasticity of demand
      3. Marginal cost
      4. Marginal propensity to consume
    4. Use rules of differentiations to find derivatives of elementary functions such as polynomial, rational, exponential and lograrithimic
    5. Compute higher derivatives and interpret their meaning
  4. Apply the chain rule to differentiate composite functions, inverse functions and functions defined implicitly.
    1. Use the chain rule to find derivatives of composite functions.
    2. Differentiate exponential,logarithmic and nth root functions
  5. Use Algebra and first and second derivatives to assist in sketching graphs of functions and use derivatives and graphs to analyze functions that model economic and business applications.
    1. Use the first and second derivatives and definitions to find critical values and inflection points
    2. Use first derivatives to find intervals of increase and decrease
    3. Use second derivatives to find intervals of concavity and inflection points.
    4. Use first and second derivative test to find local extreme values.
    5. Find absolute extreme values
    6. Use limits to define horizontal, and vertical asymptotes
    7. Use limits to define slant asymptotes (optional)
    8. use parts 1 - 7 to assist in sketching graphs of functions.
  6. Apply the first and second derivative tests to solve optimization problems including application in business and economics
    1. Solve max/min problems as the arise in theory and applications.
      1. Problems that involve exponential growth/decay
      2. Problems that involve cost, profit and revenue
    2. Find inflection points in application problems and interpret their meaning.
  7. Examine integration of functions as Riemann sums of products, such as area, and use limits of Riemann sums, antiderivatives, tables, software and numerical techniques to evaluate/approximate definite integrals.
    1. Find antiderivatives of elementary functions.
    2. Examine the concept of integration as limits of Riemann sums
      1. Interpret the definite integral as area under or between curves.
      2. study properties of definite integrals
    3. Use numerical methods and technology and to approximate definite integrals
    4. Use interaction techniques to find antiderivatives and evaluate definite integrals
      1. Antiderivatives
      2. The power rule
      3. Substitution
      4. Integration by parts
  8. Use integrations techniques to solve application problems including first order separable differential equations.
    1. Examine marginal cost, revenue, and marginal profit and their relation to cost revenue and profit respectively in applications of business management problems
    2. Solve inventory problems
    3. Use linear and exponential functions to solve depreciation problems.
    4. Use exponential functions to find present and future values.
  9. Apply rules of partial differentiation to find partial derivatives of of multivariable functions and solve optimization problems including applications in business and economics.
    1. Examine functions of two or more variables and find their domains
      1. Joint cost-output functions
      2. Joint revenue functions
      3. Joint profit functions
    2. Identify the graphs of functions in two variables as surfaces in 3D-space
    3. Find traces, and level curves of functions of two variables
    4. Compute partial derivatives of bivariate functions
      1. Bivariate production functions
      2. First marginal productivity functions
      3. First marginal productivity functions
  10. Classify improper integrals and examine their properties and use to solve applications problems
    1. Identify an improper integral as a limit at infinity
    2. Evaluate basic improper integrals
    3. Determine convergence or divergence of an improper integral
      1. Consumer surplus
      2. Accumulated present and future values of income stream
      3. Amortization of loans
      4. Finance
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