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•           Information on Degree Programmes

COURSE INFORMATON
Course Title Code Semester L+P Hour Credits ECTS
Calculus I * MT   131 1 4 5 8

 Prerequisites and co-requisites Recommended Optional Programme Components None

Language of Instruction Turkish
Course Level First Cycle Programmes (Bachelor's Degree)
Course Type
Course Coordinator Prof.Dr. Doğan DÖNMEZ
Instructors
 Prof.Dr. DOĞAN DÖNMEZ 1. Öğretim Grup:A Prof.Dr. DOĞAN DÖNMEZ 2. Öğretim Grup:A

Assistants
Goals
Defining the concepts of limit, continuity and derivative using properties of real numbers and solve maximum and minimum problems using these concepts. Approximate computation with a prescribed error.
Content
Real Numbers and their properties. Functions. Limit, continuity. Properties of continuous functions. Derivative and its applications. Sketching graphs. Finding Maxima and minima. Logarithm, exponential functions, hyperbolic functions. Inverse trigonometric and inverse hyperbolic functions. L Hospital s Rule and Taylor s Theorem with remainder.

Learning Outcomes
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Course's Contribution To Program
NoProgram Learning OutcomesContribution
12345
1
Is able to prove Mathematical facts encountered in secondary school.
X
2
Recognizes the importance of basic notions in Algebra, Analysis and Topology
X
3
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
X
4
Is able to express basic theories of mathematics properly and correctly both written and verbally
X
5
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
X
6
Expresses clearly the relationship between objects while constructing a model
X
7
Draws mathematical models such as formulas, graphs and tables and explains them
X
8
Is able to mathematically reorganize, analyze and model problems encountered.
X
9
Knows at least one computer programming language
10
Uses effective scientific methods and appropriate technologies to solve problems
11
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
12
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields
13
Knows programming techniques and is able to write a computer program
14
Is able to do mathematics both individually and in a group.

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
1 Numbers, rational and real numbers. Order. Absolute Value, number line, Intervals, inequalities. Required readings and solving problems
2 Functions, Finding the domain and range. Composition, inverse function, graphs. trigononmetric functions. Required readings and solving problems
3 Limit of a function of one variable, Limit theorems, One sided limits Required readings and solving problems
4 Infinite limits, Indefinite forms, limits at infinity, Continuity Required readings and solving problems
5 Limit criterion, Intermediate Value and Maximum-Minimum Theorems. Types of discontinuity. Required readings and solving problems
6 Derivative, slope of the tangent. Rules of differentiation. Chain Rule Required readings and solving problems
7 Higher order derivatives, Implicit differentiation. Differential and approximation using differential. Required readings and solving problems
8 Mid Term Exam Review and Solving Problems
9 Rolle s Theorem, Mean Value Theorem. Finding maxima and minima. Required readings and solving problems
10 First derivative Test, Second derivative and convexity. Second derivative test. Asymptotes. Required readings and solving problems
11 Graphing. Solving applied maxima and minima problems. Derivative of the inverse functions. Required readings and solving problems
12 Logarithm function, properties of the logarithm Required readings and solving problems
13 Exponential function. Properties of the exponential function. Required readings and solving problems
14 Trigonometric and inverse trigonometric functions. Hyperbolic functions, inverse hyperbolic functions. Required readings and solving problems
15 L Hospital s rule and Taylor s Theorem with remainder. Applications. Required readings and solving problems
16-17 FINAL EXAM Review and Solving Problems