COURSE INTRODUCTION AND APPLICATION INFORMATION


Course Name
Calculus I
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 109
Fall
2
2
3
6
Prerequisites
None
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator -
Course Lecturer(s)
Assistant(s)
Course Objectives This course aims to provide basic theory and  applications of  calculus and its extentions to mathematical analysis
Learning Outcomes The students who succeeded in this course;
  • will be able to understand conceptual and visual representation of limits, continuity, differentiability, and tangent line approximations for functions at a point.
  • will be able to calculate the first and second implicit derivatives
  • will be able to use derivatives in practical applications, such as distance, velocity, acceleration, related rates and extreme values.
Course Description Functions, limits and continuity, derivatives and its applications. extreme values, Intermediate Value Theorem, Rolle’s Theorem, The Mean Value Theorem and its applications, inverse functions and their derivatives, related rates problems.

 



Course Category

Core Courses
X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Functions and their graphs, Polynomials and rational functions. “Calculus, A complete course” by Robert A.Adams, Addison Wesley, Longman
2 Trigonometric functions, Average and instantaneous velocity, Limits of functions “Calculus, A complete course” by Robert A.Adams, Addison Wesley, Longman
3 Limits of functions, Limits at infinity and Infinite limits “Calculus, A complete course” by Robert A.Adams, Addison Wesley, Longman
4 Continuity, The formal definition of derivative “Calculus, A complete course” by Robert A.Adams, Addison Wesley, Longman
5 Tangent lines and their slopes, The derivative “Calculus, A complete course” by Robert A.Adams, Addison Wesley, Longman
6 Differentiaon rules, The chain rule “Calculus, A complete course” by Robert A.Adams, Addison Wesley, Longman
7 Derivatives of trigonometric functions, MIDTERM “Calculus, A complete course” by Robert A.Adams, Addison Wesley, Longman
8 Higher order derivatives “Calculus, A complete course” by Robert A.Adams, Addison Wesley, Longman
9 The Mean Value Theorem “Calculus, A complete course” by Robert A.Adams, Addison Wesley, Longman
10 Implicit differentiation “Calculus, A complete course” by Robert A.Adams, Addison Wesley, Longman
11 The indefinite integrals “Calculus, A complete course” by Robert A.Adams, Addison Wesley, Longman
12 Inverse functions, Exponential and logarithmic functions “Calculus, A complete course” by Robert A.Adams, Addison Wesley, Longman
13 Review
14 Review
15 Review
16 Review
Course Notes/Textbooks “Calculus, A complete course” by Robert A.Adams, Addison Wesley, Longman
Suggested Readings/Materials “Thomas’ Calculus” by Finney, Weir, Giordano

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
2
10
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
1
40
Final Exam
1
50
Total

Weighting of Semester Activities on the Final Grade
3
50
Weighting of End-of-Semester Activities on the Final Grade
1
50
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
4
64
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
16
3
Field Work
Quizzes / Studio Critiques
2
5
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
2
14
Final Exams
1
28
    Total
178

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics. X
2 To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics, X
3 To be able to define and analyze problems and to find solutions based on scientific methods, X
4 To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials, X
5 To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, X
6 To be able to criticize and renew her/his own models and solutions, X
7 To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way, X
8

To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge up-to-date, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,

X
9

To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,

X
10

To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,

X
11 To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense, X
12

By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,

X
13

To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,

14

To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,

X
15

To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 

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