Yuba Community College District

Yuba College Course Outline

### Course Information

Course Number: MATH 9
Full Course Title: Calculus for Business, Social and Life Sciences
Short Title: Calc for Bus/Soc Sci
TOP Code: 1701.00 - Mathematics, General
Effective Term: Fall 2013

### Course Standards

Course Type: Credit - Degree Applicable
Units: 4.0
Total class hours: 216.0
Total contact hours in class: 72.0
Lecture hours: 72.0
Hours outside of class: 144.0
Repeatable: No

### Minimum Qualifications for Instructors

• Mathematics (Masters Required)

### Course Description

Topics of calculus including differentiation, integration, graphs, limits, and rates. Applications from economics, business, life science, and behavioral science. Not open for credit to students with credit in Math 1A.

### Conditions of Enrollment

Satisfactory completion of: MATH 52 or MATH 52B or (Placement Exam Score)Prerequisite a satisfactory score on the mathematics placement test.

• Language - recommended eligibility for English 1A
• Mathematics - recommended eligibility for Math 52

### Content

Course Lecture Content

A. Functions and their graphs, including exponential and logarithmic functions

B.Limits and intuitive limit definition of derivative

C. Increments, tangent lines and rate of change

D. Rules of differentiation including sum, product, quotient and the chain rule

E. Implicit differentiation

F. Applications of differentiation such as marginal analysis, optimization and curve sketching

G. Antiderivatives, indefinite and definite integrals

H. Multiple techniques of integration including substitution

I. Area between curves

J. Approximating definite integral as a sum

K Applications of integration in business and economics

### Objectives

1. Find the derivatives of polynomial, rational, exponential and logarithmic functions.

2. Find the derivatives of functions involving constants, sums, differences, products, quotients and the chain rule.

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. **Requires Critical Thinking**

4. Analyze the marginal cost, profit and revenue when given the appropriate function. **Requires Critical Thinking**

5. Determine maxima and minima in optimization problems using the derivative.

6. Use derivatives to find rates of change and tangent lines.

7. Use calculus to analyze revenue, cost and profit. **Requires Critical Thinking**

8. Find definite and indefinite integrals by using the general integral formulas, integration by substitution and other integration techniques.

9. Use integration in business and economics applications. **Requires Critical Thinking**

10. Solve the differential equation with application including growth and decay. **Requires Critical Thinking**

11. Compute partial derivatives. Use Lagrange multipliers in simple constrained optimization problems. (optional)

### Student Learning Outcomes

1. Compute derivatives for polynomial functions.

### Methods of Instruction

• Lecture/Discussion
• Other
May include small group work

### Methods of Evaluation

• Exams
• Homework
• Problem Solving Exercises
• Quizzes

### Course Materials

Textbooks:
1. Barnett, Ziegler, and Byleen. Calculus for Business, Economics, Life Sciences, and Social Sciences, Twelfth ed. Prentice Hall, 2011, ISBN: 978-0-321-61399-8
Equivalent text is acceptable
Other:
1. Calculator, graphing optional Example: TI 30x or TI 83 plus