|Course Title||Code||Semester||L+P Hour||Credits||ECTS|
|Calculus II *||MT 132||2||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|
Calculating mathematical and physical quantities using integral and series summation. Introduction to functions of several variables.
Infinite Sequences and Series. Power series. Polar coordinates and parametrized curves. Indefinite and definite integral. Applications of the definite integral. Functions of several variables.
|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||Sequences, Limit. Limit theorems. Infinite limits. Monotone convergence theorem. Subsequences||Required readings and solving problems|
|2||Convergence of series. n-th term Test. Geometric series and p-series. Comparison and Limit Comparison, Ratio and Root Tests.||Required readings and solving problems|
|3||Power Series, radius of convergence. Term by term integratron of power series. Taylor and McLaurin series. Binomial Theroem.||Required readings and solving problems|
|4||Polar coordinates. Some special curves. Sketching graphs. Slope of the tangent. Parametrized curves.||Required readings and solving problems|
|5||Indefinite integral, definition and properties. Change of variable, integration by parts. Integration of some trigonometric functions.||Required readings and solving problems|
|6||Integration of some algebraic functions by substitution. Reduction formulas.||Required readings and solving problems|
|7||Integration of the rational functions. Trigonometric and some special integrals.||Required readings and solving problems|
|8||Mid Term Exam||Review and Problem Solving|
|9||Definiton and properties of definite inegral. The fundamental theorems of Calculus.||Required readings and solving problems|
|10||Change of variable formula, Improper integrals, convergence.||Required readings and solving problems|
|11||Integral Test. Finding area in rectangular and polar coordinates.||Required readings and solving problems|
|12||Calculating volume using disc and cylindirical shell methods. Arc length.||Required readings and solving problems|
|13||Area of surface of revolution. Center of mass. Pappus theorem. Functions of several variables. Limit and Continuity.||Required readings and solving problems|
|14||Maximum-Minimum Theorem. Partial derivative and differentiability. Chain Rule. Finding maxima and minima.||Required readings and solving problems|
|15||Differential Forms. Exact forms and closed forms. Gradient. Normals of level curves and level surfaces.||Required readings and solving problems|
|16-17||Final Exam||Review and Problem Solving|
|Recommended or Required Reading|
|Textbook||Analize Giriş Vol. II ; Fikri Akdeniz, Yusuf Ünlü, Doğan Dönmez|