| Course Type | Compulsory Course |
|---|
| Course Level | Bachelor's Degree |
|---|
| Year of Study | 1 |
|---|
| Semester | First Term (Fall) |
|---|
| ECTS | 7 |
|---|
| Name of Lecturer(s) |
|
| Learning Outcomes |
At the end of this course, the students;
- Will be able to solve problems related to the elementary functions and sketch their graphs.
- Know the concept of limit and continuity, make applications related to them.
- Know the concept of derivative with geometric and physical interpretations and can make applications related to derivative.
- Explain the relationship between derivative and integral.
- Solve problems related to the applications of integral.
|
| Mode of Delivery | Face to face |
|---|
| Prerequisites | No |
|---|
| Recommended Optional Programme Components | None |
|---|
| Course Description | The concept of function, definition and image sets of functions, elementary functions, graphs of functions, limit and continuity concepts in functions of one variable, asymptotes, intermediate value theorem, derivative concept in functions of one variable and differentiation rules, chain rule, closed derivative, higher order derivatives, extrema of functions, mean value theorem, L'Hospital's rule, graphing with the help of first and second derivatives, extremum problems, integral concept, indefinite integrals, integration techniques, area problem and definite integrals, area and volume calculations, arc length, improper integrals and convergence tests. |
|---|
| Course Contents |
| WEEK |
TOPICS |
|
1st Week |
Function concept, definition and image sets of functions, polynomials, rational and trigonometric functions |
|
2nd Week |
Inverse of functions; exponential, logarithmic, inverse trigonometric functions, graphs, limit concept in functions |
|
3rd Week |
Asymptotes, continuity, intermediate value theorem |
|
4th Week |
The concept of derivative in functions of one variable and derivative rules |
|
5th Week |
Chain rule, implicit derivative, logarithmic derivative, extrema of functions |
|
6th Week |
Mean value theorem, L'Hospital rule, graph drawing |
|
7th Week |
Extreme problems (optimisation) |
|
8th Week |
Midterm |
|
9th Week |
Integral: indefinite integrals, basic integration methods |
|
10th Week |
Basic integration methods |
|
11th Week |
Definite integral and its properties, fundamental theorems of integral calculus |
|
12th Week |
Applications of definite integral, area and arc length calculation |
|
13th Week |
Applications of definite integral - volume calculation |
|
14th Week |
Improper integrals and convergence tests |
|
15th Week |
General review |
|
| Recommended or Required Reading | 1. G.B.Thomas, Thomas-Calculus, 11th Edition, Addison Wesley, 2006.
2. R.A.Adams, Calculus, 4th edition, Addison Wesley, 1999.
3. Dennis G. Zill, Warren S. Wright, Matematik-Cilt 1, Çeviri Editörü: Prof. Dr. İsmail Naci Cangül, Nobel Yaynları
|
|---|
| Planned Learning Activities and Teaching Methods |
- Lecture
- Questions/Answers
- Problem Solving
|
|---|
| Assessment Methods and Criteria |
|
Quantity |
Percentage (%) |
| Mid-term |
1 |
40 |
| Quiz |
2 |
10 |
| Total(%) |
|
50 |
| Contribution of In-term Studies to Overall Grade(%) |
|
50 |
| Contribution of Final Examination to Overall Grade(%) |
|
50 |
| Total(%) |
|
100 |
|
| ECTS Allocated Based on Student Workload |
| Activities |
Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Midterm exam |
1 |
2 |
2 |
| Preparation for Quiz |
2 |
8 |
16 |
| Individual or group work |
13 |
3 |
39 |
| Preparation for Final exam |
1 |
48 |
48 |
| Course hours |
13 |
6 |
78 |
| Preparation for Midterm exam |
1 |
24 |
24 |
| Laboratory (including preparation) |
|
|
|
| Final exam |
1 |
2 |
2 |
| Homework |
|
|
|
| Total Work Load | 209 |
| Total Work Load / 30 (h) | 6.96 |
| ECTS Credit of the Course | 7 |
|
| Language of Instruction | Turkish |
|---|
| Work Placement(s) | No |
|---|
