Course Syllabus

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Catalog Description

Calculus is one of the supreme creations of the human thought. Calculus provides the tools and methods for analyzing and solving problems of change and motion quantitatively.  It introduces two new mathematical operations called differentiation and integration. Calculus I develops concepts of central importance in mathematical sciences. Calculus today continues to serve as the principal quantitative language of sciences and technologies. Calculus I involves limits and continuity of the functions, derivative and its applications, indefinite integral, definite integral and its applications.

Course Purpose:

The main purpose of Calculus I is to develop theories of derivatives, indefinite and definite integrals, associated with applications in several fields. As a result we need new fundamental concepts: limit, continuity, derivative, antiderivative, indefinite integral, and definite integral. We use the derivative theory in solving optimization problems. Scientists use definite integrals as extensively as derivatives in many different fields: in Physics, Biology, Macroeconomics, Microeconomics, Finance, Computer Sciences, etc.


Required Readings:

Main textbook: H. Anton, I. Bivens, S. Davis, Calculus, ninth edition, John Wiley & Sons, Inc., New York, 2010


Additional textbooks:

  • Howard Anton, Calculus, A new Horizon, 6th edition, John Wiley & Sons, Inc.
  • Adams, Robert A., Calculus, A complete course, 5th edition, 2003 Pearson Education Canada Inc.
  • L. Salas, Einar Hille, Calculus, one and several variables, 6th edition, John Wiley & Sons, Inc.


Course Objectives

Upon completion of this course, students should be able to:

  1. Know and apply the mathematical induction.
  2. Analyze the properties of the functions and sketch their graphs.
  3. Investigate and compute the limits using main rules and formulas.
  4. Study the continuity of the functions.
  5. Know and apply techniques of differentiation, especially the Chain Rule.
  6. Know the derivative in graphing and applications, including first and second derivative test, applied maximum and minimum problems, etc.
  7. Know and apply L’Hôpital Rule, Rolle’s Theorem, Mean-Value Theorem.
  8. Know the indefinite integrals, integration by substitution, and integration by parts.
  9. Know and apply the definite integrals, the fundamental theorem of Calculus, and principles of definite integral calculation.
  10.  Find the area enclosed by two curves, volumes by cylindrical shells, and length of a plane curve.


Content of the Course


  • Functions and Induction
    • Mathematical induction
    • Properties of functions
    • Graphing functions
    • New functions from old ones
  • Limits and continuity
    • Limits (an intuitive approach)
    • Computing limits
    • Limits (rigorous definition)
    • Continuity
    • Limits and continuity of trigonometric functions
  • The derivative
    • Slopes and rates of change
    • The derivative
    • Techniques of differentiation
    • Derivatives of trigonometric functions
    • The chain rule
    • Implicit differentiation
  • Exponential, logarithmic, and inverse trigonometric functions
    • Inverse functions, examples
    • Derivatives of logarithmic and exponential functions
    • Derivatives of inverse trigonometric functions
    • L’Hopital Rule, indeterminate forms
  • The derivative in graphing and applications
    • Analysis of functions 1: increase, decrease, and concavity
    • Analysis of functions 2: relative extrema, first and second derivative test
    • Absolute maxima and minima
    • Applied maximum and minimum problems
    • Rolle’s Theorem, Mean-Value Theorem
  • Integration
    • An overview of the area problem
    • The indefinite integral
    • Integration by substitution
    • Sigma notation; area as a limit
    • The definite integral
    • The fundamental theorem of Calculus
    • Evaluating definite integrals by substitution
  • Applications of the definite integral
    • Area between two curves
    • Volumes by slicing; disks and washers
    • Volumes by cylindrical shells
    • Length of a plane curve
  • Principals of integral evaluation
    • Integration by parts
    • Trigonometric integrals
    • Trigonometric substitutions


Course Requirements


Participation: Participation extends beyond mere attendance. Active participation is meant as the effort and the interest that a student shows in the class, including homework. After each session students are expected to study all the relevant material, read all the associated exercises, identify the difficult points and pose their questions in the next session either directly to me or in the class. You may miss up to three classes without penalty – your first two absences count whether you have a good excuse or not. Each absence beyond the first three will cost you points off of your participation grade. The only exceptions to this rule are severe illness (doctor’s note required) and UNYT approved trips/activities. Appropriate documentation for absences beyond the first three is necessary the class day directly before or after the one you miss. You are expected to attend class and I do keep attendance records. In general: this class is intensive and interactive. Missing class could seriously affect your grade! Students who are absent more than 20% of the total hours of the semester (i.e. 12 hours) may be required to withdraw from the course.


Class conduct: Exams are closed books. Also, you use your own calculator and nothing else will be allowed. Mobile phones are strictly not tolerated in the class for any use (including computations). Cheating and plagiarism in any form will result immediately in the grade F.

Students are responsible for everything that is announced, presented or discussed in class. The way to avoid any misunderstanding associated with this course is to attend class. Please, be courteous during class; both to me and your colleagues. I find late arrivals distracting, which cause a decline in the quality of my lecture. Importantly, it is also disruptive to your colleagues. Please, refrain from talking during class; it is disruptive to your colleagues and the lecture. I expect the best behavior from all of you. This is what education is all about. Please, consider that the language of instruction is English, so all our conversation into the class must be in this language.


Exams: Two examinations will be taken, a midterm exam during week seven of the course and a final exam covering all course content during the final examination period. Exam format may combine a mixture of short answer, true/false, matching, sort answer, and reasoning problems covering all readings, lecture, hand-out and class discussion content. Another test will be included in the period between the midterm and final exam.


Final Examination: Friday, February 5, 2016, Time: 9:00 -11:00.  


General Requirements

Deadlines in submitting the homework are critical. Therefore, late assignments and absence from tests will not be tolerated.   In the event of illness or emergency, contact your instructor IN ADVANCE to determine whether special arrangements are possible. The University’s rules on academic dishonesty (e.g. cheating, plagiarism, submitting false information) will be strictly enforced. Please familiarize yourself with the STUDENT HONOUR CODE, or ask me or your advisor for clarification.



Criteria for Determination of Grade


Active Participation 10%
Homework 10%
Midterm exam  30%
Test 20%
Final exam 30%


Grading scale follows the official UNYT as below:


Letter Grade Percent (%) Quality Points Generally Accepted Meaning
           A 96-100 4.00 Outstanding work
           A- 90-95 3.67
           B+ 87-89 3.33 Good work, distinctly above average
           B 83-86 3.00
           B- 80-82 2.67
           C+ 77-79 2.33 Acceptable work
           C 73-76 2.00
           C- 70-72 1.67
           D+ 67-69 1.33 Work that is significantly below average
           D 63-66 1.00
           D- 60-62 0.67
           F 0-59 0.00 Work that does not meet minimum standards for passing the course



Technology Expectations: usage of power-point, excel, word.  Students must keep copies of all assignments and projects sent by e-mail.

Assignments are to be word-processed and converted into pdf files. Continuing and regular use of e-mail is expected.


STUDENTS: If you feel that you have encountered special learning difficulties or serious problems that interfere with your studies, please make an appointment with UNYT Counseling Center, Dr. E Cenko ( and/or the Academic Support Center, Dr. A Canollari ( They are trained to help students with learning difficulties and have offered to provide this service to our students, just as it is offered in all American universities; you can also discus with your academic advisor.

If you need help with course content, please refer to the Math Center. Please feel free to talk to me for additional information.




Date Prepared: October 02/2015

Prepared by Prof. Dr. Fejzi Kolaneci



Faculty: Business &Economics.

Department: Maths & N.Sciences.

Grade: Undergraduate.

Majors: Business and Computer Sciences.

Study Fileds: Accounting, Computer Science, Economics, Finance, and Management of Information Systems.

Course Year: 2.

Course Program: UNYT.

Scheduele: Wednesday & Friday 9:00-11:00, Class 2E.

Instructor: Prof. Dr. Fejzi Kolaneci

Credits: 4

Prerequisite: College Algebra & Trigonometry