|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 Coordinator||Prof.Dr. Doğan DÖNMEZ|
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.
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.
|Course's Contribution To Program|
|No||Program Learning Outcomes||Contribution|
Is able to prove Mathematical facts encountered in secondary school.
Recognizes the importance of basic notions in Algebra, Analysis and Topology
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
Is able to express basic theories of mathematics properly and correctly both written and verbally
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
Expresses clearly the relationship between objects while constructing a model
Draws mathematical models such as formulas, graphs and tables and explains them
Is able to mathematically reorganize, analyze and model problems encountered.
Knows at least one computer programming language
Uses effective scientific methods and appropriate technologies to solve problems
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
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
Knows programming techniques and is able to write a computer program
Is able to do mathematics both individually and in a group.
|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|
|Recommended or Required Reading|
|Textbook||Analize Giriş Cilt I ; Fikri Akdeniz, Yusuf Ünlü, Doğan Dönmez|