Course Syllabus Math 1316
MATHEMATICS FOR ECONOMICS AND BUSINESS ANALYSIS
TTh Spring 20XX
This course satisfies the University of Texas at Arlington core curriculum requirement in mathematics.
This course will address three objectives:
 Critical Thinking Skills - to include creative thinking, innovation, inquiry, and analysis, evaluation and
synthesis of information.
 Communication Skills - to include effective development, interpretation and expression of ideas through
written, oral and visual communication.
 Empirical and Quantitative Skills - to include the manipulation and analysis of numerical data or
observable facts resulting in informed conclusions.
INSTRUCTOR:
Office Phone:
OFFICE:
E-Mail:
TEXT: Mathematical Applications for the Management, Life, and Social Sciences ; 10th edition; Custom Edition for
University of Texas at Arlington, Harshbarger & Reynolds
Course Learning Goals/Objectives: To develop mathematical tools that are useful in analysis of business and economics
problems. The topics include: supplementary Math of Finance, Differential and Integral calculus. After this course, the students
should have an understanding of Interest, Annuities, Differential and Integral calculus sufficient to apply to real problems in
Business and Finance. Chapters 5, 6, 9, 10, 11, 12, 13 will be covered. Course Prerequisites: Math 1315 or equivalent.
Course Learning Outcomes: Upon completion of Math 1316, students will be able to perform the following tasks.
1.
2.
Students will be able to compute the limit of various functions without the aid of a calculator.
Students will be able to determine whether a function is continuous or discontinuous. Students will be able to determine
where a function is discontinuous.
3. Students will be able to compute the derivative and antiderivative of various functions ( polynomial functions, rational
functions, exponential functions and logarithmic function) without the aid of a calculator, and interpret certain limits as
derivatives. In particular, they will be able to compute derivatives using differentiation techniques such as chain rule,
product rule, quotient rule and power rule; they will be able to compute certain antiderivatives using various
antidifferentiation techniques such as integration by substitution. Students will be able to use integration to find total
area.
4. Students will be able to solve word problems involving applications to business such as marginal analysis. Students will
be able to maximize revenue, given the total revenue function. Students will be able to minimize the average cost, given
the total cost function. Students will be able to find the maximum profit from total cost and total revenue functions, or
form a profit function.
5. Students will be able to find the equation of the tangent line to the graph of a function at a point by using the derivative
of the function.
6. Students will be able to sketch the graphs of functions by finding and using first-order, and second-order, critical points
and extrema.
7. Students will be able to solve optimization problems in the context of real-life situations by using differentiation and
critical points of functions. Students will be able to apply the procedures for finding maxima and minima to solve
problems from management, life, and social sciences.
8. Students will be able to apply the Fundamental Theorems of Calculus to compute definite integrals and area.
9. Students will be able to compute the future value of investments with simple and compound interest. Students will be
able to compute the future and present values of ordinary annuities. Students will be able to compute the payment
required in order for ordinary annuities to have a specified future value and to compute the payments of a specified
present value for an ordinary annuity.
10. Students will be able to compute the regular payments required to amortize a debt and the amount that can be
borrowed for a specified payment.
11. Students will be able to use integration to find total cost functions from information involving marginal cost. Students
will be able to optimize profit, given information regarding marginal cost and marginal revenue.
OFFICE HOURS: 1:00 –2:00 pm T Th; (Other times available by appointment.)
Homework: Homework will be assigned on a daily basis. Assigned problems will be listed on an assignment sheet.
Homework will not be taken up and graded but will be gone over in lab each week and at the end of lectures if there is
time available. The answers to the assigned problems can be found at the back of the text since the problems assigned
are odd problems. You will also be given a class key you can use to gain access to online homework assignments located
at www.webassign.com. The online homework assignments are roughly equivalent to the homework problems assigned
from your text. You can either elect to do the online homework assignments, the problems form your text assigned on
the assignment sheet, or a combination of the two. No matter which you elect to do (online homework or assigned
problems from the text book) all homework is simply for practice and will not be turned in for a grade. Your grade will be
determined from you lab quiz grades, major test grades, final exam, and assigned extra credit opportunities.
Homework needs to be done in order to be successful in this class. All tests and quizzes will be based on the assigned
homework problems and if you can do the homework you should be able to do well on them.
Quizzes/Signature Assignment:
There will be 11 weekly quizzes given at weekly labs . All quizzes will be of
a multiple choice format and a scantron form 815-E will be required for all quizzes. Students need to provide their
own scantrons for quizzes. Quizzes will be open book and open note. They will be no more than 4 or 5 questions
and usually last no more than 10 minutes. The 2 lowest of the 11 quiz grades will be dropped. The remaining 9 quiz
grades will be averaged and this average will count as a 4th major test grade. No make-ups will be given for quizzes. If
you miss a quiz you must use it as one of your 2 dropped quiz grades. For more information on these quizzes see the
lab policy statement. To specifically assess the core objectives of Critical Thinking, Communication, and Empirical and
Quantitative Reasoning, all students will complete a signature assignment (described at the end of this syllabus),
which will count for one quiz grade.
Tests:
There will also be 3 major tests given in this class. The approximate dates for these tests are given on the
assignment sheet. [ As the instructor for this course, I reserve the right to adjust this schedule in any way that serves the
educational needs of the students enrolled in this course.] All tests will be of a multiple choice format and a scantron
form 882-E will be required for all tests. Students need to provide their own scantrons for tests. Tests will be closed
book but calculators and a 4 by 6 note card will be allowed. You will be given a detailed review sheet before each major
test. This review sheet will include a practice test. The average of your best 9 quiz grades will serve as a 4th major test
grade.
Grading: The lowest of the 4 major test grades will be dropped. The average of the 3 remaining test grades will
count 70% and the final exam will count 30%. The final exam can not be dropped. Students are expected to keep
track of their performance throughout the semester and seek guidance from available sources (including the
instructor) if their performance drops below satisfactory levels.
Final Exam: There will also be given a comprehensive departmental final exam.
The date for the final exam is
Saturday May 4th . This date needs to be kept open for the final so put it on your calendars and schedule around it.
Makeups for the final will only be granted on a limited basis and only when written documentation verifying the need
for the makeup is provided. The exact location for the final exam will be announced in class at a later date.
Calculators: A good scientific calculator or a graphing calculator is needed for this class. You will not be allowed to
use your cell phone, laptop calculator, any calculator that has texting capability, a TI 89, or a TI NSPIRE on a test or
quiz. [otherwise you can use whatever calculator you prefer.]
Bonus Problems:
Bonus problems will be given periodically throughout the semester. They will be made available
on Blackboard shortly before each major test and it will be announced during lecture class when these problems
become available. They will typically open up on a Thursday and close on a Tuesday. Points awarded for these bonus
problems will be added onto the next upcoming major test. No bonus problems will be allowed to be turned in late.
Attendance:
Attendance will not be taken on a daily basis but in order to do well students need to plan to attend
lecture and labs on a regular basis. The course is comprehensive and it will be hard to catch up if you fall behind.– You
are also responsible for keeping up with all major test dates. We will attempt to stay on schedule but occasionally we
might get behind and have to catch up later. Changes in schedule will be posted on Blackboard.
Test Corrections: You will also be given the opportunity to do test corrections on the first 2 major tests in order to
earn 5 extra points per test. To do test corrections you must go to lab to pick up your test and work on them their with
your lab instructor. The lab instructor will collect the papers and get them to me. There will be no time to do test
corrections on the third major test, but any student who turns in corrections for the 1st 2 major tests will automatically
be given 5 points added to the 3rd test grade.
Make up Tests : No make-ups will be given for quizzes. If you miss a quiz you must use it as one of your 2 dropped
quiz grades. Neither will make-ups be allowed for major test grades unless you miss the test due to participation in a
sport or other campus activity to which I have been given documentation verifying the conflict. If you miss a test due to
an above mentioned conflict it is up to you to e-mail me or call me and arrange to makeup the test prior to the end of
the next regularly assigned class period. Anyone can arrange to take a test early if they know they are going to have to
be absent for a justifiable reason. Otherwise if you miss a major test the grade, it will have to be used as your one
dropped test grade. . Anyone who misses more than one test grade needs to make an appointment to talk to me during
office hours.
Blackboard:
We will be making use of Blackboard in this class. Copies of our syllabus, assignment sheet, lab policy,
and lab quiz schedule will all be located here under the syllabus section. In addition under the course content section
students wil find copies of lecture notes and review sheets for tests. Quiz and test grades will also be posted here.
Students should periodically log onto Blackboard in order to check on their grades. To access the course, go to
http://elearn.uta.edu/ and log in with your NetID and password. Click on the name of the course in the upper left
module after logging in. They need to e-mail me or their lab instructors if they have any questions about their grades.
All graded papers returned to students should be kept in a safe place until the end of the semester in case they are
ever needed to resolve a grade dispute.
DROP POLICY:
Students may drop or swap (adding and dropping a class concurrently) classes through selfservice in MyMav from the beginning of the registration period through the late registration period. After the late
registration period, students must see their academic advisor to drop a class or withdraw. Undeclared students must
see an advisor in the University Advising Center. Drops can continue through a point two-thirds of the way through
the term or session. It is the student's responsibility to officially withdraw if they do not plan to attend after
registering. Students will not be automatically dropped for non-attendance. Repayment of certain types of
financial aid administered through the University may be required as the result of dropping classes or withdrawing.
For more information, contact the Office of Financial Aid and Scholarships (http://wweb.uta.edu/ses/fao).
The last day for students to drop is Friday 5/29/2013.
NEED HELP:
1) Math Clinic –located on 3rd floor PKH
2) The science lab has tapes you can listen to on many of the various topics covered in this course . It is
located at (106 Life Science Building).
3) See me during office hours or by appointment
4) A list of private tutors may be found in the Math Office or Cost Share tutoring is provided by the
university if you call 817-272-2617.
Math1316 Signature Assignment
[This assignment allows students to demonstrate skills they have learned in this course. It gives them a
chance to demonstrate their understanding of the finance, differential calculus, and integral calculus
topics covered in this class and h0w these topics can be applied to solve real world business problems.
These skills will be further developed and utilized in subsequent economics and business classes that the
students choose to take.]
Students will be assigned a selection of three problems from the sample problems below, representing three
conceptual foci of MATH 1316. Following each question, the students will need to answer the question: what 3
primary mathematical concepts were fundamental to your solution of this problem? Justify your answer.
1. A loan of $2000 with an interest rate of 15% compounded annually is to be repaid by making annual
payments at the end of each year for the next 4 years. Construct an amortization schedule for this loan?
Period
0
1
2
3
4
Payment
Interest
Balance Re duction UnpaidBala nce
2. For 20 years I invest $200 a month into an account that pays 3% compounded monthly. At the end of this 20
year period I invest the closing balance in an annuity from which I want to be able to make equal quarterly
withdrawals for the next 25 years . What is the accumulated amount in the account after the first 20 years?
What is the maximum size of withdrawals that I can make at the end of each quarter from my annuity account
for the next 25 years without running out of capital if the going rate of interest for this account for this period is
considered to be 4.04% compounded quarterly. After the last withdrawal the balance in this account will be
zero. What is the total amount of money able to be withdrawn from the annuity over the 25 years
a) Accumulated amount in the account after the 1st 20 years
______
____________
b) Maximum quarterly withdrawal amount that can be made from the accumulated balance for the next 25 years
__________________
c) Total amount of money withdrawn from annuity over the 25 years
__________________
3. You own an 5 year, 5 1/2% simple interest bearing note with a face value (principal) of $15,000. Three
months before the due date of the note you need some money due to an unexpected emergency and decide to
sell the note to a friend. If your friend wants to earn 8% simple interest on their investment, how much should
your friend agree to pay you for the note?
__________________
4. You own a 10 year 6% simple interest bearing note with a face value (principal) of $10,000. If you decide to
sell the note two years early and receive a sale price of $14,000 for the note, what simple interest rate did you
actually earn for the 8 years that you owned the note? Give answer to the nearest whole percent.
__________________
5. You deposit $100 at the end of each quarter in a sinking fund earning 4% compounded quarterly. How many
quarterly deposits must you make in order to reach your goal of saving 25,000? Round your answer off to the
nearest whole number.
__________________
6. For 20 years I invest $100 a month into an account that pays 4.5% compounded monthly. At the end of this
time I close out the account and invest the closing balance for the next 25 years in an account paying 5.5%
compounded continuously. What is the accumulated amount in the account at the end of the 45 year period?
Round your answer off to the nearest penny
__________________
7. Find the lim
x 6
18  3x
x  4 x  12
2
____________
8. Use the definition f x   lim
h 0
f x  h   f x 
to find the derivative of
h
f x   2 x 2  3x  8 . (You
must show your work and compute the derivative using the above formula in order to get credit for your
answer)
9. Find the equation for the tangent line to the function f ( x)  4 x 2  3x  1 when x = 2.
______________________
10. Given y = [(x3)(x2 + 1)]3 calculate the instantaneous rate of change of this function when x = 2.
The instantaneous rate of change is __________?
11. Find the derivative of y 
300 x  300
. Leave your final answer in simplified factored form.
(2 x  3) 2
12. An electronic manufacturing company has determined that the cost of producing x units of its newest stereo
is C(x) = 3500 + 10x, and the monthly demand equation is p  40 
1
x where x is the number of units
1500
and p is the price in dollars. Use the demand equation to find the revenue equation. Then find the profit
equation, and find and interpret the marginal profit for a production level of 7500 units.
R(x) = ____________________________________________
P(x) =_____________________________________________________
Marginal profit when x = 7500 _____________________
Interpretation of the above marginal profit: ______________________________________________
13. Given y = 1/6 x6 - x4 +7 find the x value where the relative maximum of this equation occurs.
The relative maximum occurs when x = ____________?
14. Given MR = 200 – 4x, MC = 80 + 2x, and the total cost of producing 10 items is $1200, find the optimal
level of production, R(x), C(x), P(x), and the maximum profit.
Optimal Level of Production ______________________________________
R(x) = __________________________________________________________
C(x) =_____________________________________________________________
P(x) = ________________________________________________________________________
Maximum profit = ______________________________________________________________
15. Find the equilibrium point, the consumer’s surplus, and the producer’s surplus if the demand function is
p(x) = f(x) =
200  .4 x 2 and the supply function is p(x) = g(x) = .1x
2
.
Equilibrium point __________________
Consumer’s Surplus _______________
Producer’s Surplus ___