| Course Description |
|
| Course Name |
: |
Calculus II |
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| Course Code |
: |
MT 132 |
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| Course Type |
: |
Compulsory |
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| Level of Course |
: |
First Cycle |
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| Year of Study |
: |
1 |
|
| Course Semester |
: |
Spring (16 Weeks) |
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| ECTS |
: |
8 |
|
| Name of Lecturer(s) |
: |
Assoc.Prof.Dr. ALİ ARSLAN ÖZKURT
|
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| Learning Outcomes of the Course |
: |
Can compute limits of sequences
Can determine the convergence of an infinite series
Can express functions as power series
Can recognize and sketch different curves.
Can compute indefinite integrals
Can compute definite integrals.
Can compute area, volume, arc length, surface area and center of mass using definite integral.
Can find the limits of functions of several variables.
Can compute partial derivatives of functions of several variables.
Can find maxima and minima of functions of several variables.
|
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| Mode of Delivery |
: |
Face-to-Face |
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| Prerequisites and Co-Prerequisites |
: |
None |
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| Recommended Optional Programme Components |
: |
None |
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| Aim(s) of Course |
: |
Calculating mathematical and physical quantities using integral and series summation. Introduction to functions of several variables. |
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| Course Contents |
: |
Infinite Sequences and Series. Power series. Polar coordinates and parametrized curves. Indefinite and definite integral. Applications of the definite integral. Functions of several variables. |
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| Language of Instruction |
: |
Turkish |
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| Work Place |
: |
Classroom |
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Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
|
1 |
Sequences, Limit. Limit theorems. Infinite limits. Monotone convergence theorem. Subsequences |
Required readings and solving problems |
Lecturing and discussion |
|
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 |
Lecturing and discussion |
|
3 |
Power Series, radius of convergence. Term by term integratron of power series. Taylor and McLaurin series. Binomial Theroem. |
Required readings and solving problems |
Lecturing and discussion |
|
4 |
Polar coordinates. Some special curves. Sketching graphs. Slope of the tangent. Parametrized curves. |
Required readings and solving problems |
Lecturing and discussion |
|
5 |
Indefinite integral, definition and properties. Change of variable, integration by parts. Integration of some trigonometric functions. |
Required readings and solving problems |
Lecturing and discussion |
|
6 |
Integration of some algebraic functions by substitution. Reduction formulas. |
Required readings and solving problems |
Lecturing and discussion |
|
7 |
Integration of the rational functions. Trigonometric and some special integrals. |
Required readings and solving problems |
Lecturing and discussion |
|
8 |
Definiton and properties of definite inegral. The fundamental theorems of Calculus. |
Required readings and solving problems |
Lecturing and discussion |
|
9 |
Mid Term Exam |
Review and Problem Solving |
Written Exam |
|
10 |
Change of variable formula, Improper integrals, convergence. |
Required readings and solving problems |
Lecturing and discussion |
|
11 |
Integral Test. Finding area in rectangular and polar coordinates. |
Required readings and solving problems |
Lecturing and discussion |
|
12 |
Calculating volume using disc and cylindirical shell methods. Arc length. |
Required readings and solving problems. |
Lecturing and discussion |
|
13 |
Area of surface of revolution. Center of mass. Pappus theorem. Functions of several variables. Limit and Continuity. |
Required readings and solving problems |
Lecturing and discussion |
|
14 |
Maximum-Minimum Theorem. Partial derivative and differentiability. Chain Rule. Finding maxima and minima. |
Required readings and solving problems |
Lecturing and discussion |
|
15 |
Differential Forms. Exact forms and closed forms. Gradient. Normals of level curves and level surfaces. |
Required readings and solving problems |
Lecturing and discussion |
|
16/17 |
Final Exam |
Review and Problem Solving |
Written Exam |
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|
| Contribution of the Course to Key Learning Outcomes |
| # | Key Learning Outcome | Contribution* |
|
1 |
Is able to prove Mathematical facts encountered in secondary school. |
5 |
|
2 |
Recognizes the importance of basic notions in Algebra, Analysis and Topology |
3 |
|
3 |
Develops maturity of mathematical reasoning and writes and develops mathematical proofs. |
2 |
|
4 |
Is able to express basic theories of mathematics properly and correctly both written and verbally |
5 |
|
5 |
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. |
5 |
|
6 |
Expresses clearly the relationship between objects while constructing a model |
5 |
|
7 |
Draws mathematical models such as formulas, graphs and tables and explains them |
4 |
|
8 |
Is able to mathematically reorganize, analyze and model problems encountered. |
4 |
|
9 |
Knows at least one computer programming language |
3 |
|
10 |
Uses effective scientific methods and appropriate technologies to solve problems |
0 |
|
11 |
Knows programming techniques and is able to write a computer program |
0 |
|
12 |
Is able to do mathematics both individually and in a group. |
0 |
|
13 |
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians |
0 |
|
14 |
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 |
0 |
| * Contribution levels are between 0 (not) and 5 (maximum). |
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