Chabot College
Fall 2008
Removed Fall 2010
Course Outline for Math 32
CALCULUS FOR BUSINESS AND SOCIAL SCIENCES
Catalog Description:
32 – Calculus for Business and Social Sciences
5 units
Functions and their graphs; differential and integral calculus of polynomial, rational, exponential and
logarithmic functions; partial derivatives. Applications in business, economics and the life and social
sciences. Prerequisite: Mathematics 55, 55L or 55B (completed with a grade of C or higher) or an
appropriate skill level demonstrated through the Mathematics Assessment process. 5 hours. 0-1 hours
laboratory.
[Typical contact hours: lecture 87.5, laboratory 0-17.5]
Prerequisite Skills:
Before entering the course the student should be able to:
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perform basic operations on complex numbers;
solve quadratic equations by factoring, completing the square, and quadratic formula;
find complex roots of a quadratic equation;
sketch the graphs of functions and relations:
a. algebraic, including polynomial and rational
b. logarithmic
c. exponential
d. circles;
find and sketch inverse functions;
perform function composition;
solve exponential and logarithmic equations;
apply the concepts of logarithmic and exponential functions;
solve systems of linear equations in three unknowns using elimination and substitution;
apply the properties of and perform operations with radicals;
apply the properties of and perform operations with rational exponents;
solve equations and inequalities involving absolute values;
solve equations involving radicals;
graph linear inequalities in two variables;
find the distance between two points;
find the midpoint of a line segment.
Expected Outcomes for Students:
Upon completion of the course the student should be able to:
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graph polynomial, rational, exponential and logarithmic functions;
find limits numerically, graphically, and using limit properties;
determine intervals of continuity graphically and using continuity properties;
differentiate using the definition of the derivative;
differentiate using the rules of differentiation including the chain rule;
find equations of tangent lines;
find marginal cost, marginal revenue and marginal profit;
find all maxima, minima and points of inflection;
solve applied optimization problems;
differentiate implicitly;
solve related rate problems;
integrate using basic rules of integration;
integrate by substitution;
integrate by parts;
evaluate definite integrals;
find the area under and between curves;
solve applied exponential growth and decay problems;
Chabot College
Course Outline for Mathematics 32, page 2
Fall 2008
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evaluate improper integrals;
find first and second order partial derivatives of functions of two variables;
solve optimization problems using partial derivatives;
Course Content:
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Functions
a.
Definition
b.
Notation
c.
Domain and range
d.
Graphs and graphing transformations
Types of functions
a.
Linear functions and equations of lines
b.
Quadratic functions
c.
Polynomial functions
d.
Rational functions
e.
Exponential and logarithmic functions
Limits
a.
Definition
b.
One-sided
c.
Infinite
Continuity
a.
Definition at a point and over an interval
b.
Properties of continuity
c.
Discontinuity
d.
One-sided
Derivative
a.
Definition
b.
Geometric interpretation
c.
Notation
d.
Rules of differentiation, including chain rule
e.
Second derivatives
f.
Implicit differentiation
Application of the derivative
a.
Maximum-minimum problems
b.
Curve sketching
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Related rates
d.
Marginal analysis
Integration
a.
Antiderivatives
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Area under a curve and the definite integral
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The Fundamental Theorem of Calculus
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Techniques of integration
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Improper integrals
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Applications
Partial differentiation
a.
Functions of several variables
b.
Maximum-minimum problems
c.
Applications
Methods of Presentation:
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Lectures
Problem Solving
Discussions
Chabot College
Course Outline for Mathematics 32, page 3
Fall 2008
Assignments and Methods of Evaluating Student Progress:
1. Typical Assignments
a. A company manufactures and sells x television sets per month. The monthly cost and pricedemand equations are
C ( x)  72,000  60 x
x
p  200 
0  x  6,000
30
(a) Find the maximum revenue.
(b) Find the maximum profit, the production level that will realize the maximum profit, and the
price the company should charge for each television set.
b. The weekly marginal cost of producing x pairs of tennis shoes is given by
C ' ( x)  12 
500
x 1
where C(x) is cost in dollars. If the fixed costs are $2,000 per week, find the cost function. What
is the average cost if 1,000 pairs of shoes are produced each week?
c. A firm produces two types of calculators, x thousand of type A and y thousand of type B per
year. If the revenue and cost equations for the year are (in millions of dollars)
R ( x, y )  2 x  3 y
C ( x, y)  x 2  2 xy  2 y 2  6 x  9 y  5
determine how many of each type of calculator should be produced per year to maximize profit.
What is the maximum profit?
2. Methods of Evaluating Student Progress
a. Homework
b. Quizzes
c. Exams
d. Final Examination
Textbook(s) (Typical):
Applied Calculus, Soo Tan, Brooks Cole, 2005
Special Student Materials:
Scientific or graphing calculator
Prior: Dec 1998
Revised: 9/17/08