MATH 47S - Calculus for Business with Support
MATH 47S
4 units
Calculus for Business with Support
54 hours lecture, 54 hours laboratory
Prerequisite: MATH 40 or MATH 40S
Grading: letter grade.
Description
This course is a study of differentiation of functions of one and several variables, optimization methods, integration of functions of one variable, and exponential and logarithmic functions. The course is appropriate for students who wish to pursue a career in business and economics. The course also includes the foundational skills and support necessary to complete business calculus.
Transferability
Transferable to both UC and CSU; see counselor for limitations
Identifiers & Codes
Department: Math & Engineering
School: Science, Engineering & Mathematics
Academic Level: Undergraduate
TOP Code: 170100 - Mathematics, General
CTE Status: No
SAM Code: E - Non-Occupational
CIP Code: 27.0101 - Mathematics, General.
Credit or Noncredit: Credit
Class Size Max, Units, Hours
Class Size Maximum: 40
Lecture Hours: 3
Lab Hours: 3
Supplemental Hours: 0
Credit Units: 4
Out of Class Hours: 6
Weekly In-Class Hours: 6
Teaching Units: 6
Total Student Learning Hours: 324
Total Contact Hours: 216
Requisites & Limitations on Enrollment
Prerequisites: MATH 40 or MATH 40S
Catalog Information
Grade Mode: Letter Grade
Are there Materials Fees for the course? No
Is the course repeatable? No
Student Learning Outcomes & Course Objectives
Student Learning Outcomes:
- 1. Interpret and evaluate derivatives of various functions of one or multiple variables using rules of derivatives and apply in graphing and in real world problems such as growth, decay, optimization, and elasticity of demand.
- 2. Evaluate definite and indefinite integrals using the Fundamental Theorem of Calculus, and apply in real world problems such as Area, Net Change, Average, and Surplus.
Course Objectives:
1. Define function, domain, and range.
2. Define the limit of a function.
3. Evaluate the limit of a function.
4. Define continuous functions.
5. Define the derivative of a function.
6. Find the derivative of a function using the definition of the derivative.
7. Use derivatives to find rate of change and tangent lines.
8. Employ the rules of differentiation, including the Product Rule, Quotient Rule, Chain Rule, and Power Rule.
9. Evaluate marginal functions.
10. Evaluate higher order derivatives.
11. Identify increasing and decreasing functions, convexity and concavity in order to sketch graphs of functions.
12. Identify critical points.
13. Find absolute maxima and minima of a function.
14. Distinguish relative maxima and minima using the second derivative test.
15. Solve maximum profit, maximum revenue, and minimum cost problems.
16. Solve by implicit differentiation and find related rates.
17. Differentiate exponential and logarithmic functions.
18. Evaluate elasticity of demand and other applications from business and economics.
19. Define the antiderivative of a function.
20. Apply basic integration rules to find all antiderivatives of a function.
21. Evaluate definite integrals using the Fundamental Theorem of Calculus.
22. Approximate definite integrals as sum of areas.
23. Use Lagrange multipliers to solve maximum and minimum problems with constraints.
24. Demonstrate an understanding of the underlying skills necessary for business calculus.
2. Define the limit of a function.
3. Evaluate the limit of a function.
4. Define continuous functions.
5. Define the derivative of a function.
6. Find the derivative of a function using the definition of the derivative.
7. Use derivatives to find rate of change and tangent lines.
8. Employ the rules of differentiation, including the Product Rule, Quotient Rule, Chain Rule, and Power Rule.
9. Evaluate marginal functions.
10. Evaluate higher order derivatives.
11. Identify increasing and decreasing functions, convexity and concavity in order to sketch graphs of functions.
12. Identify critical points.
13. Find absolute maxima and minima of a function.
14. Distinguish relative maxima and minima using the second derivative test.
15. Solve maximum profit, maximum revenue, and minimum cost problems.
16. Solve by implicit differentiation and find related rates.
17. Differentiate exponential and logarithmic functions.
18. Evaluate elasticity of demand and other applications from business and economics.
19. Define the antiderivative of a function.
20. Apply basic integration rules to find all antiderivatives of a function.
21. Evaluate definite integrals using the Fundamental Theorem of Calculus.
22. Approximate definite integrals as sum of areas.
23. Use Lagrange multipliers to solve maximum and minimum problems with constraints.
24. Demonstrate an understanding of the underlying skills necessary for business calculus.
Course Content
Course Content:
I. Review of functions and their graphs, lines and exponents
2 Hour(s)
II. Derivatives and their Applications
A. Limits and continuity
B. Tangent and secant lines
C. Rates of change, slopes of tangent lines, and derivatives
D. Differentiation rules including sum, power, constant product rules
E. The product, quotient, and chain rules and the generalized power rule
F. Higher-order derivatives
G. Non-differentiable functions
B. Tangent and secant lines
C. Rates of change, slopes of tangent lines, and derivatives
D. Differentiation rules including sum, power, constant product rules
E. The product, quotient, and chain rules and the generalized power rule
F. Higher-order derivatives
G. Non-differentiable functions
10 Hour(s)
III. Applications of Derivatives
A. Graphing using the first and second derivatives
B. Marginal analysis
C. Optimization applications
D. Optimizing cost, revenue, and profit, lot size and harvest size
E. Implicit differentiation and related rates
B. Marginal analysis
C. Optimization applications
D. Optimizing cost, revenue, and profit, lot size and harvest size
E. Implicit differentiation and related rates
10 Hour(s)
IV. Exponential and Logarithmic Functions
A. Exponential functions
B. Logarithmic functions
C. Differentiation of logarithmic and exponential functions
D. Applications to economics such as elasticity of demand
B. Logarithmic functions
C. Differentiation of logarithmic and exponential functions
D. Applications to economics such as elasticity of demand
8 Hour(s)
V. Integration and its Applications
A. Antiderivatives and indefinite integrals
B. Integration rules such as the power, sum, and constant product rules and antiderivatives for logarithmic and exponential functions
C. Definite integrals and areas
D. Approximating definite integral as sum of areas
E. Applications of definite integrals such as average value and area between curves
F. Applications to business and economics, such as consumer's surplus and continuous streams of income
G. Integration by substitution and integration by parts techniques
B. Integration rules such as the power, sum, and constant product rules and antiderivatives for logarithmic and exponential functions
C. Definite integrals and areas
D. Approximating definite integral as sum of areas
E. Applications of definite integrals such as average value and area between curves
F. Applications to business and economics, such as consumer's surplus and continuous streams of income
G. Integration by substitution and integration by parts techniques
14 Hour(s)
VI. Calculus of Several Variables
A. Functions of several variables
B. First and second order partial derivatives
C. Optimizing functions of several variables using the D-test
D. Lagrange multipliers and constrained optimization
B. First and second order partial derivatives
C. Optimizing functions of several variables using the D-test
D. Lagrange multipliers and constrained optimization
10 Hour(s)
VII. Algebra content, as needed, in the context of the skills for the following topics:
1. Review of functions and their graphs, lines and exponents
2. Derivatives and their applications
3. Applications of derivatives
4. Exponential and logarithmic functions
5. Integration and its applications
6. Calculus of several variables
2. Derivatives and their applications
3. Applications of derivatives
4. Exponential and logarithmic functions
5. Integration and its applications
6. Calculus of several variables
54 Hour(s)
Methods of Instruction & Active Learning
Instructional Method(s):
- Other
Examples: The overall scope of instruction is to use a combination of lecture, discussion, and collaborative learning. Homework questions are addressed, new concepts are introduced and explained, and students are then typically given problems to solve together. Students are then assigned homework problems to work on before the next class.
For the lab portion of this class, students will complete instructor-led activities reviewing algebra skills as needed for the business calculus content.
For example, students work collaboratively to find the limit of a function using a graphing utility. Group and whole class discussions are used to solve applications and evaluate the methods used in arriving at a solution.
Assignment for In and Out of Class
Assignment Types:
- Substantial college level writing assignment, such as: essay(s), written homework, term/research paper, and/or other (Required).
- Substantial college level reading assignment, such as: textbook, journal article(s), literature, and/or other (specify)
- Lab or field activity, product, and/or report
- Group Assignment
- Other
Examples: Application problems are assigned that require the student to set up a function, input data and compute results, sketch the results graphically, and interpret the results. Written homework is required to develop skills needed in problem solving applications.
Textbook reading is required on a weekly basis.
Students will complete instructor-led activities reviewing algebra skills as needed for the business calculus content.
Group assignments are given so that students can set up, solve and present solutions to real world application problems.
A group assignment requires students to collectively analyze information given in the problem description and use this information with mathematical concepts and methods acquired to develop a solution for that problem.
Students can use the internet to research topics in business, economics, life sciences, and social sciences. Their findings can be presented to the class to show the application of calculus to real world topics.
Methods of Evaluation
Computational or Non-Computational Problem Solving Demonstrations:
- Exam(s)
- Quizzes
- Homework Problem(s)
- Other
Further Methods of Evaluation:
- Objective examinations, such as: multiple choice, true/false, matching items, completion
Examples: Exams, including a final exam, will be given to evaluate the students' mastery of definitions, knowledge of technical skills of limits, derivatives, and integrals, and application of these skills to problem solving.
Quizzes will be evaluated on the student's ability to analyze key concepts, apply key concepts, and solve problems as they relate to content. Quizzes will assess a content area that is of a smaller scope than exams.
Assignments will be evaluated on the completion of the assignment in a timely manner, thorough and correct completion of the assignment based on the instructions given, and signs of effort in the completion of the assignment.
Laboratory activities may be evaluated on participation, collaboration, and completeness.
Parts of exams may use objective questions in order to evaluate the student's mastery of vocabulary and course content.
Diversity, Equity, Inclusion, Accessibilty
Mathematics and Engineering instruction includes approaches to teaching that promote inclusion and engagement with diverse bodies of students. Instructional methods welcome diverse perspectives, aim to close equity gaps, and are accessible to all students, as all fields benefit from Mathematics and Engineering instruction that values thoughts from individuals with diverse backgrounds and experiences.
Teaching faculty participate in college-wide efforts to close equity gaps, such as course-level data validation in program planning, centers and communities for teaching, DEIA professional development activities, and Student Learning Outcomes assessment.
Cyclical Routine Review of course objectives, outcomes, content, assignments, methods of evaluation, methods of instruction, representative textbooks and materials, and requisites allows faculty to explore how each element of the course outline illustrates inclusion and engagement with diverse student bodies.
Course instruction is accessible to all students and is achieved through professional development support, and District accessibility procedures which guarantee accommodation so that all students can equally participate in learning opportunities.
Design of instructional materials, including those hosted online in learning management systems, can be reviewed for accessibility through supportive systems technology that meet best practices for Accessibility and Universal Design for Learning (UDL).
Representative Textbooks and Materials
Representative Textbook:
Brief Applied Calculus. Geoffrey Berresford & Andrew Rockett. 7th Edition. Cengage. 2016.
As of July 2024, the 7th edition is the most current edition and according to the publisher, no new editions are in plan.
Open Educational Resources (OER):
Business Calculus, LBCC Custom Edit, Simone Nguyen & Robert Kemp, 1st edition. OER. 2020.