VYSOKA SKOLA MANAZMENTU
Syllabus
MTH 219V
CALCULUS AND FINANCIAL MATHEMATICS
5 credits
Effective
Copyright 2010
Vysoká škola manažmentu/City University of Seattle
All rights reserved
REQUIRED RESOURCES
Tan, S. T. (2005). College mathematics for the managerial, life, and social sciences (6th ed.).
Brooks/Cole-Thomson Learning.
Whitaker, A. (2010). Research and APA style guide. Bratislava, Slovakia: City University of Seattle.
Available for purchase in the library or available for download at http://www.vsm.sk/en
/students/academic-support/
Access to a personal computer and the Internet is required. All written assignments must be word-processed.
MTH 219V
MATHEMATICS FOR BUSINESS
This document provides an overview of the course foundation elements and assignments. If you have
additional questions about the course, please contact your instructor.
SCHOLASTIC HONESTY POLICY
City University of Seattle/Vysoká škola manažmentu expects each student to do his/her own work.
CU/VŠM has "zero tolerance" for cheating, plagiarism, unauthorized collaboration on assignments
and papers, using "notes" during exams, submitting someone else's work as one's own, submitting
work previously submitted for another course, or facilitating acts of academic dishonesty by others.
The penalties are severe! A first offense can result in a zero grade for the course and suspension for
one quarter; a second offense can result in a zero grade for the course and suspension for two or more
quarters; a third offense can result in expulsion from CU/VŠM. The Policy and Procedures may be
found at http://www.vsm.sk/en/students/scholastic-honesty/policies-and-procedures/.
In addition to providing your work to the instructor for grading, you must also submit an electronic
copy for the CU/VŠM archives (unless the work is specifically exempted by the instructor). You will
not receive a grade for particular work until and unless you submit this electronic copy. The
procedure for submitting work to the archives is to upload it via the website
http://www.vsm.sk/en/students/on-line-center/uploader/uploader.html. Files should include the cover
page of the work with the student name, instructor name, course name and number, and date. File
names should indicate the type of assignment, such as “researchpaper.doc”, “casestudy.doc” or “
thesis.doc” (student name should not be a part of the file name because the system adds it). All files
received into the archives are submitted to www.TurnItIn.com for plagiarism checking.
COURSE DESCRIPTION
This course will concentrate on calculus of one real variable and foundations of financial
mathematics. The optimization theory based on the first and the second-derivative test, respectively,
are discussed. Applications in the area of production functions and managerial decisions are
mentioned. Special types of functions, analysis of their properties and rules of differentiation are
covered in the problems. Rate of interest, annuities, amortization and sinking funds are discussed in
financial mathematics.
CORE CONCEPTS, KNOWLEDGE, AND SKILLS
Function of a real variable, graph of a function, domain. Inverse function, polynomial function,
rational function, exponential function, logarithms, functions and economic analysis. The first and the
second derivative. Finding minimum and maximum extrema, optimization based on the first-
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derivative test and the higher derivative test. Analysis of functions. Production functions. Rate of
interest, annuities, amortization and sinking funds.
COURSE OUTCOMES
Upon the successful completion of this course, students will be able to:
 Understand the notions of function, graph of a function, inverse function and logarithm;
 Find a domain of a function;
 Analyze functional properties and to interpret results in economic analysis;
 Understand a geometrical definition of derivative;
 Use the rules of differentiations;
 Analyze a simple production function;
 Solve optimization problems by the first-derivative test and the higher derivative tests,
respectively;
 Solve exponential and logarithmic equations;
 Solve problems on financial mathematics involving rate of interest, annuities,
amortization and sinking funds.
RECOMMENDED SUPPLEMENTARY RESOURCES
As a City University of Seattle/Vysoká škola manažmentu student, you have access to library
resources regardless of where and how you are taking this class. To access the resources necessary to
complete your coursework, visit the library menu in the My.CityU portal at https://my.cityu.edu, and
the CU Slovakia library home page at http://library.cutn.sk/. For additional help, visit the library or
submit your question in the Contact Us section of the Slovakia library’s web site.
Electronic Resources
The following Internet resources may be of use to you in this course. Please be aware that addresses
may change from time to time. Consult with your instructor if you have questions about electronic
resources.
Vysoká škola manažmentu : http://www.vsm.sk
Math.com: The World of Math Online : www.math.com
Wolfram MathWorld : http://mathworld.wolfram.com/
Calculus of One Real Variable – a tutorial : http://www.phengkimving.com/
CyberEcon : The Production Function : http://ingrimayne.com/econ/TheFirm/ProductionFunct.html
OVERVIEW OF COURSE GRADING
The grade you receive for the course will be derived using City University of Seattle/Vysoká škola
manažmentu’s decimal grading system, based on the following:
Assignments
Percentage of Final Grade
SIA
7 online homework assignments (OHW)
Optimization Task
Midterm Exam
Final Exam
0%
28%
6%
33%
33%
TOTAL
100%
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SPECIFICS OF COURSE ASSIGNMENTS
STUDENT INTRODUCTORY ASSIGNMENT
City University/Vysoká škola manažmentu requires that you submit a Student Introductory
Assignment (SIA). This SIA must be completed during the first week of your course. The SIA
consists of introducing yourself in the Discussion Forum titled: Student Introductory Assignment. It is
designed to begin the online class experience by letting us know you are in class and facilitating
interaction. It is due at the end of the first week. Even though this assignment is not graded, it is
required in order for you to continue your course. Your instructor will notify CU/VSM at the end of
the first week as to whether or not you completed your SIA.
7 ONLINE HOMEWORK ASSIGNMENTS
In weeks 2-4 and 6-9 you will work out a short task related to the material covered in the given week
and post your clear answer on the BB. Some of these tasks will be based on a calculation of a problem
chosen from a given set, and some will require a real-life example about a given topic. The number of
given tasks will be equal to the number of students in the section. Each task can be chosen/posted only
once; thus, each student must check all previous postings and the last student must calculate/post the
last remaining task.
You will not only be responsible for completing your part of the assignment on time, but you are also
expected to check the completed work of your classmates. This means that after posting your own
answer, you are supposed to correct one student’s answer. Check another student’s work (again, each
task should be checked once), and post on the BB whether you think the student is correct or not, and
explain why. This does not mean you have to re-calculate the problem on the BB, but rather explain
where you think the student made a mistake. Only students who post their own calculation are
allowed to check classmate’s work.
VERY IMPORTANT: In each week, a list of all the problems will be posted on Monday; you must
post your calculation by Thursday, and your response to a classmate’s calculation must be posted
either on Friday or Saturday. Earlier corrections will not be graded. The calculations must be posted
on time; otherwise, they will be graded with 0%. Only students who participate in PART I are allowed
to participate in PART II. No reservations are possible, all attachments must be attached together with
a message, a maximum time difference is 15 minutes. No make-ups for these will be given and the
corresponding BB folder will be closed after the due date.
Grading Criteria for Online Homework
Completion of homework
Appropriate response to classmates’ work
50%
50%
OPTIMIZATION TASK
At the end of the trimester, each student will be required to calculate one optimization problem. A
clear and transparent solution will be required. All detailed instructions and an example will be posted
on May 23. The paper must be uploaded at http://www.vsm.sk/sk/studenti/online-centrum/uploader/
by May 27. Only uploaded papers will be graded. Do not send it to me by email.
Grading Criteria for Optimization Problem
Determining the objective function
Finding a derivative of the objective function
Evaluating the absolute extrema
Appropriate organization and format
40%
20%
30%
10%
MIDTERM AND FINAL EXAM
You will take a midterm and a final exam in the course to reinforce the course materials. The exams
will test your ability to utilize statistical terminology as well as the identification and application of
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proper statistical tools for a given statistical problem. The midterm will cover the first five weeks of
the course, the final exam will deals with the material of weeks 6-9. Each exam will be scheduled for
2 hours, all formulas will be provided by the instructor and students must have the calculators. The
exams cannot be combined together.
Students can discuss any problems referring to these on the BB in advance. Complete calculations
will be checked, not just final results, and students will get partial credit for following the right steps.
If you are not available on the given day and you have a serious reason for it, you have to discuss a
date for a make-up exam with me IN ADVANCE. If you do not do this, I have to grade your exam
with 0%.
PROCTORED EXAMINATIONS
This course is offered from the Trencin CU/VŠM site, and all exams will be given by the instructor at
this site.
If you are a student registered at the other CU/VŠM site and would like to take your exams there, you
may use the CU/VŠM Proctor Center. However, you must inform your instructor about your interest
in taking exams at the Proctor Center before Friday of Week 3. Students who do not inform their
instructor on time cannot use the Proctor Center and must travel to the instructor’s site.
BEWARE: As of Fall 2008, the school applies a change in the proctoring policies - the students
residing in Slovakia cannot have an external proctor anymore.
If you are a student residing outside Slovakia and you cannot take the exams in either Bratislava or
Trenčín, you must find a proctor (e.g. local library head, local university instructor), fill out the
Proposed Proctor Approval Request Form (http://www.vsm.sk/files/studenti/Proctor-FormCU.pdf), and submit the form to your Associate Dean for approval before Friday, Week 3. Also
notify your instructor that you have submitted a proctor form. Proctor forms submitted after the
deadline will not be accepted and you will be required to take the exam with your instructor.
HOT NEWS: As of the Spring 2011, the school is offering a possibility to take midterm and
final exams via a newly approved proctor in Presov, Ing.Sylvia Jencova, PhD. In case you
want to use this option, let me know in SIA by the end of week 1. However, the exams still
have to be written on the official date stated in this document.
All exams proctored abroad, in Bratislava, and Presov, will be held the same day as here in
Trencin and the proctor must be able to send your exam back to me on the same day. Please,
ask your proctor to contact me as the first otherwise I cannot send any materials.
COURSE POLICIES
You are responsible for understanding and following all of City University of Seattle/Vysoká škola
manažmentu’s academic policies. If you want more information about VŠM policies, consult the
VŠM catalog.
Attendance
Students taking courses in any format are expected to attend class regularly. This is important in
achieving learning outcomes in the course and may be a valid consideration in determining the final
grade.
Late Assignments
Students are expected to turn in assignments on time. All late assignments will be graded with 0%.
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RECOMMENDED COURSE SCHEDULE
WEEK
1
TOPICS AND ASSIGNMENTS
READINGS
Review.
Algebraic expressions. Functions and their properties.
Graphs of functions, domain of functions.
Tan, ch. 9.3,
Tan, ch. 10.1
SIA
2
Types of functions and their properties.
Quadratic and polynomial functions.
The inverse function and its graph.
Fundamentals of economic analysis functions
Tan, ch. 10.1, 10.2, 10.3
OHW1
3
Derivatives.
The notion of the derivative and its geometrical meaning.
Rules of differentiations.
Tan, ch. 11.1-11.3, 11.5
OHW2
4
Rules of differentiations and applications of derivatives.
Minimum/maximum finding using the first and the second
derivative tests.
Concavity of function.
Tan, ch. 11.4, 12.1, 12.2
OHW3
5
Curve Sketching.;
Tan, ch. 12.3
Midterm Exam, May 5, at 16.00
6
Optimization problems.
Analysis of functions and production functions.
Tan, ch. 12.4, 12.5
OHW4
7
Exponential and logarithmic functions and their graphs.
Exponential and logarithmic equations.
Tan, ch. 13.1-13.2
OHW5
8
The financial mathematics foundations.
Rate of interest, Annuities
Tan, ch. 5.1, 5.2
OHW6
Optimization Task
9
Financial mathematics.
Amortization and sinking funds.
Tan, ch. 5.3
OHW7
10
Review.
Final Exam, June 9, at 16.00
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