| Course Description |
|
| Course Name |
: |
Calculus I |
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| Course Code |
: |
MT 131 |
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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 |
: |
Fall (16 Weeks) |
|
| ECTS |
: |
8 |
|
| Name of Lecturer(s) |
: |
Assoc.Prof.Dr. ALİ ARSLAN ÖZKURT
|
|
| Learning Outcomes of the Course |
: |
Expresses theorems related to limits.
Defines continuity and expresses related theorems
Solves problems using some of the properties of continuous functions.
Define and computes derivatives.
Computes some irrational numbers approximately.
Finds the maximum and minimum of functions of one variable and sketches their graphs.
Solves applied maximum and minimum problems.
|
|
| 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 |
: |
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. |
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| Course Contents |
: |
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. |
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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 |
Numbers, rational and real numbers. Order. Absolute Value, number line, Intervals, inequalities. |
Required readings and solving problems |
Lecturing and discussion |
|
2 |
Functions, Finding the domain and range. Composition, inverse function, graphs. trigononmetric functions. |
Required readings and solving problems |
Lecturing and discussion |
|
3 |
Limit of a function of one variable, Limit theorems, One sided limits |
Required readings and solving problems |
Lecturing and discussion |
|
4 |
Infinite limits, Indefinite forms, limits at infinity, Continuity |
Required readings and solving problems |
Lecturing and discussion |
|
5 |
Limit criterion, Intermediate Value and Maximum-Minimum Theorems. Types of discontinuity. |
Required readings and solving problems |
Lecturing and discussion |
|
6 |
Derivative, slope of the tangent. Rules of differentiation. Chain Rule |
Required readings and solving problems |
Lecturing and discussion |
|
7 |
Higher order derivatives, Implicit differentiation. Differential and approximation using differential. |
Required readings and solving problems |
Lecturing and discussion |
|
8 |
Rolle´s Theorem, Mean Value Theorem. Finding maxima and minima. |
Required readings and solving problems |
Lecturing and discussion |
|
9 |
Mid Term Exam |
Review and Solving Problems |
Written Exam |
|
10 |
First derivative Test, Second derivative and convexity. Second derivative test. Asymptotes. |
Required readings and solving problems |
Lecturing and discussion |
|
11 |
Graphing. Solving applied maxima and minima problems. Derivative of the inverse functions. |
Required readings and solving problems |
Lecturing and discussion |
|
12 |
Logarithm function, properties of the logarithm |
Required readings and solving problems |
Lecturing and discussion |
|
13 |
Exponential function. Properties of the exponential function. |
Required readings and solving problems |
Lecturing and discussion |
|
14 |
Trigonometric and inverse trigonometric functions. Hyperbolic functions, inverse hyperbolic functions. |
Required readings and solving problems |
Lecturing and discussion |
|
15 |
L´Hospital rule and Taylor´s Theorem with remainder. Applications. |
Required readings and solving problems |
Lecturing and discussion |
|
16/17 |
FINAL EXAM |
Review and Solving Problems |
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. |
2 |
|
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 |
5 |
|
8 |
Is able to mathematically reorganize, analyze and model problems encountered. |
4 |
|
9 |
Knows at least one computer programming language |
0 |
|
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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