Download MATH 75, Mathematical Analysis for Business

City College of San Francisco
Course Outline of Record
I. GENERAL DESCRIPTION
A. Approval Date
B. Department
C. Course Number
D. Course Title
E. Course Outline Preparer(s)
April 2014
Mathematics
MATH 75
Mathematical Analysis for Business
Glenn Aguiar, Matt Bertens, & Guy De
Primo
F. Department Chair
Dennis
G. Dean
David
II. COURSE SPECIFICS
A. Hours
B. Units
C. Prerequisites
Corequisites
Advisories
D. Course Justification
E. Field Trips
F. Method of Grading
G. Repeatability
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Lecture: 3 weekly (52.5 total)
3
MATH 60 or MATH 860 or MATH 92
None
None
This course meets a transfer requirement for
students majoring in business, especially
tbose transferring to San Francisco State
University.
No
Letter
o
III. CATALOG DESCRIPTION
Linear, quadratic, algebraic, exponential, and logarithmic functions with applications to business
and economics; interest and ordinary annuity problems; introduction to differential and integral
calculus of one variable with applications to business and economics.
IV. MAJOR LEARNING OUTCOMES
Upon completion of this course a student will be able to:
A. Graph, write, and interpret linear equations in two vallables.
B. Create linear snpply and demand models; create linear or quadratic cost, revenue, and
profit models; and interpret model information.
C. Analyze and solve interest and ordinary annuity problems.
D. Calculate derivatives and interpret their values as instantaneous rates of change or as
slopes oftangent lines.
E. Calculate and interpret marginal functions.
F. Analyze and solve absolute extremum problems involving cost, revenue, or profit.
G. Find a function given its derivative and a function value, and fmd the total change of a
function given its derivative, in the context of business applications.
CCSF, Mathematics, MATH 75, Mathematical Analysis for Business, April 20 14, Page 1 of 4
V.CONTENTS
A. Algebra topics
1. Linear equations in two variables
a. Definitions
b. Slopes and intercepts
c. Fonn (slope-intercept or point-slope)
d. Finding linear equations
e. Graphs (lines)
2. Logarithms
a. Definition
b. Logmithmic - exponential conversions
c. Properties
d. Logmithmic and exponential equations (simple)
e. Natmal and common logarithms
B. Functions
1. Function basics
a. Definition
b. Function representations (e.g., table, graph, equation)
c. Domains and ranges (emphasis on domains)
d. Function notation and evaluation
2. Quadratic functions
a. Definition
b. Vertex and intercepts
c. Graphs (parabolas)
3. Algebraic functions
a. Types (polynomial, rational, radical)
b. Graphs (by plotting points)
4. Exponential functions
a. Definition
b. Domains and ranges
c. Graphs
5. Logarithmic functions
a. Definition
b. Domains and ranges
c. Graphs
6. Business models
a. Cost, revenue, and profit, when plice is independcnt of quantity
b. Supply and demand
c. Equilibrium analysis
d. Cost, revenue, and profit, when price varies linearly with quantity
e. Break-even analysis
C. Mathematics of finance
1. Simple Interest
a. Definitions and fOIIDulas
b. Using the fonnulas to solve for interest, amount, principal, tern1, or simple interest
rate
CCSF, Mathematics, l\.1ATH 75, Mathematical Analysis for Business, April 2014, Page 2 of 4
2. Compound Interest
a. Definitions and formulas
b. Using the fmIDulas to solve for amount, principal, number of payments, term,
periodic intcrest rate, or interest
c. AIIDual percentage rate (yield) calculations
d. Continuous compounding
3. Ordinary annuities: future value and sinking funds
a. Definitions and formulas
b. Using the formulas to solve for future value, periodic paymcnt, number of
payments, or term
4. Ordiuary annuities: present value and amortization
a. Definitions and formulas
b. Using the formulas to solve for present value, periodic payment, number of
payments, or term
c. Recommended if time: amortization schedules, equity, and remaining balance
calculations
D. Derivatives
1. Limits
a. Intuitive introduction
b. Finding limits given a function's graph
c. Limit theorems (motivated, not proved)
d. Using the theorems to find limits for simple algebraic functions
2. Continuity
a. Definitions
b. Finding where functions represented by graphs or by algebraic equations are
continuous
c. Finding where functions represented by graphs or by algebraic equations are
discontinuous
3. Derivative and interpretations
a. Definitions
b. Instantaneous rate of change of a function
c. Slope of a tangent line to a curve at a point
4. Differentiation
a. Basic rules including the power rule
b. Product, quotient, and chain rules
c. Rules for the natural exponential and logarithmic functions
d. Using the rules to differentiate combinations of functions
E. Applications of the derivative
1. Instantaneous velocity
2. Equation oftangent line to a curve
3. Marginal analysis (marginal cost, revenue, profit, demand, and supply)
4. Curve sketching (using derivatives to find critical numbers, increasing and decreasing
behavior, local extrema, and concavity)
5. Absolute extrema: emphasis on minimizing cost and maximizing revenue and profit
F. Integrals
1. Antiderivatives and indefinite integrals
a. Definitions
CCSF, Mathematics, MATH 75, Mathematical Analysis for Business, April 2014, Page 3 of 4
b. Fonnulas (empbasis on the power lUle) and properties
c. Calculate indefinite integrals of simple algebraic fmlctions
d. Finding a function when given the function's derivative and one function value
(emphasis on business applications)
2. Total change
a. Finding the total change in a quantity by using the fundamental theorem of calculus
b. Finding a total change in a function between two given domain values when given
the function's derivative (emphasis on business applications)
VI. INSTRUCTIONAL METHODOLOGY
A. Assignments
1. In-class assignments: discussion, individualized work, or small group work appropriate
to the day's lesson
2. Out-of class assignments
a. Reading assignments for the material being covered in class
b. Regular homework that provides students with review and practice on the topics and
procedures taught, such as graphing and interpreting functions, calculations
involving compound interest, and evaluation and interpretation of derivatives
c. Group work may be required at the discretion of the instlUctor
B. Evaluation
1. Assignments as described above
2. Periodic exams that assess each student's proficiency in topics such as break-even
analysis; equilibrium analysis; quadratic function applications involving optimization
of revenue and profit; applications involving simple annuities; and calculation of
derivatives and integrals
3. A comprehensive final examination coveling key topics such as sketching and
interpreting graphs offllilctions; applications involving present and future values;
differentiation and marginal analysis; and simple applications of integration
C. Textbooks and other instlUctional materials
1. Textbook
a. Raymond A. Bamett, Michael R. Zeigler, and Karl E. Byleen, College Mathematics
for Business, Economics, Life Sciences and Social Sciences, 12th edition, Pearson
Education, Inc., Upper Saddle River, New Jersey, 2011, Custom Edition for City
College of San Francisco
b. See the Mathematics Department's textbook list for the current textbook
2. Other instlUctional materials
a. A scientific or graphing calculator may be required
b. Computer software and internet access may be required for problem-solving and
exerCIses
c. InstlUctor developed notes or exercises
VII. TITLE 5 CLASSIFICATION
CREDIT/DEGREE APPLICABLE (meets all standards of Title 5. Section 55002(a)).
CCSF, Mathematics, I\1ATH 75, Mathematical Analysis for Business, APli12014, Page 4 of 4