Discipline: Mathematics
Originator: Jeff Warsinski

# Riverside Community College District Integrated Course Outline of Record

Mathematics 5
 MAT-5 : Calculus for Business and Life Science College: RIV NOR MOV Lecture Hours: 72.000 Outside-of-Class Hours: 144.000 Units: 4.00 Grading Methods: Pass/No Pass Letter Grade
Course Description
Prerequisite: MAT-35 or appropriate placement.
Course Credit Recommendation: Degree Credit

A study of the techniques of calculus for majors in business, business administration, life and social sciences. Emphasis on problem solving and applications. Topics include: Functions, graphs, limits, derivatives, integrals, exponential and logarithmic functions. 72 hours lecture. (Letter Grade or Pass/No Pass option.)
Short Description for Class Schedule
Entrance Skills:
Before entering the course, students should be able to demonstrate the following skills:
1. Apply the basic operations of algebra on the set of real numbers, polynomials, rational and radical expressions.
• MAT-35 - Simplify algebraic expressions using correct mathematical symbols and language.
2. Solve linear, rational, quadratic, exponential, radical, logarithmic, absolute value equations, and systems of equations.
• MAT-35 - Identify and apply appropriate methods to solve rational, radical, exponential, and logarithmic equations.
3. Graph equations of lines and linear inequalities; graph basic functions.
• MAT-35 - Graph linear and basic nonlinear functions.
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities:
1. Find the derivatives of polynomial, rational, exponential and logarithmic functions.
2. Determine the limit of a function at a point and at infinity.
3. Sketch the graph of functions using horizontal and vertical asymptotes, intercepts, and first and second derivatives to determine intervals where the function is increasing and decreasing, maximum and minimum values, intervals of concavity and points of inflection.
4. Use calculus to analyze cost, revenue and profit functions; find the marginal cost, revenue and profit when given appropriate functions.
5. Use derivatives to find rates of change and tangent lines.
6. Find definite and indefinite integrals by using general integration formulas, integration by substitution and other techniques.
7. Apply integration to the solution of business, economics and life science problems.
8. Find the derivatives of functions involving constants, sums, differences, products, quotients, and the chain rule.
9. Determine maxima and minima in optimization problems using the derivative.
Student Learning Outcomes:
Upon successful completion of the course, students should be able to demonstrate the following skills:
1. Determine the limit of a function.
2. Find the derivatives of functions.
• Critical Thinking: Students will be able to demonstrate higher-order thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
3. Determine definite and indefinite integrals.
4. Use calculus to find solutions to business, economics and life science applications.
• Critical Thinking: Students will be able to demonstrate higher-order thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
General Education Outcomes:
• CSU GE Area B: Physical and its Life Forms(mark all that apply) - B4 - Mathematics/Quantitative Thinking
• UC/CSU Transfer Course - Yes
Course Content:
1. Functions, Graphs, and Limits
1. Graphs of functions including exponential and logarithmic
2. Limits at a point and infinity
3. Continuity of Functions.
4. Intuitive limit definition of derivative.
2. Differentiation
1. Slope of a tangent line, rate of change, increments
2. Basic Rules of Differentiation
3. Product and Quotient Rules
4. Chain Rule
5. Higher-Order Derivatives
6. Implicit Differentiation
3. Applications of the Derivative
1. Increasing and decreasing functions, extrema, concavity
2. Optimization
3. Business, Life and Social Science applications
4. Marginal analysis
5. Curve sketching
6. Related Rates (Optional)
4. Exponential and Logarithmic Functions
1. Derivatives
2. Exponential growth and decay
3. Compound interest
5. Integration Techniques
1. Antiderivative, indefinite and definite integrals
2. Substitution
3. Approximating definite integrals as a sum
6. Applications of Integration
1. Area between curves
2. Business, Life and Social Science
Methods of Instruction:
Methods of instruction used to achieve student learning outcomes may include, but are not limited to, the following activities:
• Lectures/presentations/ demonstrations with question and answer periods that both disseminate information and pose problems in calculus for administration, business, life and social science.
• Showing films or videos, distributing handouts, using calculators and manipulatives, using computers, and/or using electronic or computer-based media in order to reinforce understanding of concepts related to calculus for administration, business, life and social science.
• Cooperative/collaborative learning tasks and activities designed to assist students in mastering the techniques of differentiation and integration
• One-to-one tutoring and guided practice in solving problems in marginal analysis and optimization.
• Computer-assisted, graphics calculators and/or web-enhanced instruction for finding tangent lines, rates of changes and definite integrals with numerical methods.
Methods of Evaluation:
Students will be evaluated for progress in and/or mastery of student learning outcomes using methods of evaluation which may include, but are not limited to, the following activities:
• Individual and group assignments including problem sets, essays, reports, projects, and calculator/computer assignments designed to demonstrate successful understanding and application of basic concepts and definitions in calculus for administration, business, life and social science.
• Quizzes/examinations designed to assess students’ ability to recall, critically analyze and apply differentiation to rate of change problems and marginal analysis.
• Participation in class discussions to ensure progress in mastering graphing functions using first and second derivatives.
• Participation in collaborative learning projects and problem sets to demonstrate mastery of calculus for administration, business, life and social science.
• Midterm and final examination designed to assess students’ mastery and ability to devise, organize and present complete solutions to calculus problems for business and life science.
Sample Assignments:
• Reading of the textbook, handouts, and lecture notes on the applications of the derivative and integral pertaining to business and life science.
Outside-of-Class Writing Assignments
• Problem sets requiring students to present complete solutions to optimization, rates of change, and applications of integration.
• Graphing functions using asymptotes, intercepts, extrema, and concavity.
Other Outside-of-Class Assignments
• Review of study guides and homework problems on the applications of differentiation and integration.
Course Materials:
All materials used in this course will be periodically reviewed to ensure that they are appropriate for college level instruction. Possible texts include the following:
• Barnett, Ziegler, Byleen. Applied Calculus for Business, Economics, Life Sciences and Social Sciences. 13th Pearson, 2015.
• Hughes-Hallett. Applied Calculus. 6th Wiley, 2018.
• Tan, Soo. Applied Calculus for the Managerial, Life, and Social Sciences. 10th Thomson Learning, 2015.
• Graphics calculator such as Texas Instruments TI-84
• Software appropriate for Business/Life Science calculus.
Codes/Dates:
CB03 TOP Code: 1701.00 - Mathematics, General
CB05 MOV Transfer Status: N/A (not in college inventory) (D)
CB05 NOR Transfer Status: Transfers to Both UC/CSU (A)
CB05 RIV Transfer Status: Transfers to Both UC/CSU (A)
C-ID#: MATH 140
Board of Trustees Approval Date: 04/16/2019
COR Rev Date: 04/16/2019