Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Compulsory
Objectives of the Course Calculus course is an introduction to the basic mathematical techniques that have been proved to be useful in analyzing problems in physics and engineering. Limit and derivative are among the topics which are taught in the course. This course supplies a strong background for mathematics students.
Course Content
Functions and their graphs, trigonometric and exponential functions, inverse functions, limit and continuity of a function of a single variable, introduction to derivative of a function, implicit differentiation and chain rule, the basic theorems of differential calculus: Intermediate Value, Extreme
Value, and the Mean Value Theorems, applications of derivative: graph sketching and problems of extrema, related rate and optimization problems.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Associate Prof.Dr. ORHUN KARA
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources 1. J. Hass, M. Weir, G. Thomas, UNIVERSITY CALCULUS, Addison Wesley, 2007 2. Thomas G, M. Weir, J. Hass, Thomas’ Calculus. Early Transcendentals, Pearson Education, 2009
1) Thomas’ CALCULUS, N-th Editions, (N = 1,2,…,11) 2) Ayres F, Mendelson E, Schaum’s outline of Calculus, McGraw-Hill, 1990 3) Apostol T.M. Calculus and Linear Algebra, Wiley, 1967 4) Marsden J, Weinstein A. Calculus Unlimited, Benjamin,1981 5) Dunham W. The Calculus Gallery: Masterpieces from Newton to Lebesgue, 2004. 6) Silverman R.A. Essential Calculus and Analytic Geometry, Dover, 2003

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 40
Quizzes 1 % 10
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 50
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 56 56
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 1 56 56
Application (Homework, Reading, Self Study etc.) 1 34 34
Exams and Exam Preparations 1 75 75
Total Work Load   Number of ECTS Credits 7 221

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 The ability to understand and apply mathematical techniques for solving problems
2 To distinguish mathematical language to solve concrete problems
3 To be able to write and speak about subjects
4 The ability to demonstrate knowledge of basic mathematical theorems
5 To be able to prove basic mathematical theorems

Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 The Real Numbers and Real Line
2 Functions and their Graphs
3 Trigonometric Functions and Their Inverses
4 Exponential Functions
5 Rates of Changes and Limits
6 Limit of a Function and Limit Laws ; Precise Definition of a Limit
7 One-sided Limit and Continuity
8 Tangents and Derivative at a Point; Derivative as a Function and Differentiation Rules
9 The Derivative as a Rate of Change and Derivatives of Trigonometric Functions
10 The Chain Rule and Implicit Differentiation
11 Derivatives of Inverse Functions Particularly those of Logarithmic Functions and Trigonometric Functions ; Related Rates along with Linearization and Differentials
12 Extreme Values of Functions and The Mean Value Theorem
13 Monotonic Functions and the First Derivative Test; : Concavity and Curve Sketching
14 Indeterminate Forms and L’Hopital’s Rule ; Applied Optimizations
15 Final 1st week
16 Final 2nd week

Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 3
C2 4 3
C3 4 3
C4 4
C5 4

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant