- Course Code
- EMT104
- Semester
- Second Term (Spring)
- Theory+Practice
- 4 + 2
- ECTS
- 8
| Course Type | Compulsory Course |
|---|
| Course Level | Bachelor's Degree |
|---|
| Year of Study | 1 |
|---|
| Semester | Second Term (Spring) |
|---|
| ECTS | 8 |
|---|
| Name of Lecturer(s) |
|
| Learning Outcomes |
At the end of this course, the students;
- Know the rules of limit in multivariable functions.
- Solve problems related to the continuity of functions of several variables.
- Interpret the concept of partial derivative geometrically and solve related questions.
- Calculate area and volume with the help of double integrals.
|
| Mode of Delivery | Face to face |
|---|
| Prerequisites | No |
|---|
| Recommended Optional Programme Components | Calculus 1 |
|---|
| Course Description | The concept of multivariable function, definition and value sets of functions, function graphs, limits and continuity in functions of two variables, partial derivative in functions of two variables, chain rule, directional derivative, gradient and tangent plane concepts are given. Local extremum values, absolute extremum values and their applications. Lagrange multipliers, double integral concept, area and volume calculations with double integrals (in Cartesian and polar coordinates) are discussed. |
|---|
| Course Contents |
| WEEK |
TOPICS |
|
1st Week |
Functions of several variables, topology of R^n |
|
2nd Week |
Domain and range of multivariable functions, graphs, level curves |
|
3rd Week |
Limit and continuity |
|
4th Week |
Continuity |
|
5th Week |
Derivatives of functions of several variables, partial derivatives, chain rule |
|
6th Week |
Implicit derivative, higher order derivatives |
|
7th Week |
Directional derivative, gradient, tangent plane and normal line |
|
8th Week |
Midterm |
|
9th Week |
Extremums of multivariable functions and applications |
|
10th Week |
Lagrange multipliers |
|
11th Week |
The concept of double integral |
|
12th Week |
Area and volume calculations with double integral |
|
13th Week |
Double integrals in polar coordinates |
|
14th Week |
Double integrals in polar coordinates |
|
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. Zii, Warren S. Wright, Calculus, Matematik Cilt II, Çeviri Editörü: Prof. Dr. İsmail Naci Cangül
|
|---|
| 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 |
10 |
20 |
| Individual or group work |
13 |
6 |
78 |
| Preparation for Final exam |
1 |
32 |
32 |
| Course hours |
13 |
6 |
78 |
| Preparation for Midterm exam |
1 |
28 |
28 |
| Laboratory (including preparation) |
|
|
|
| Final exam |
1 |
2 |
2 |
| Homework |
|
|
|
| Total Work Load | 240 |
| Total Work Load / 30 (h) | 8 |
| ECTS Credit of the Course | 8 |
|
| Language of Instruction | Turkish |
|---|
| Work Placement(s) | No |
|---|
Programme Qualifications / Learning Outcomes
|
LO1 |
LO2 |
LO3 |
LO4 |
| K1 |
|
|
X |
|
| K2 |
|
|
|
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| K3 |
|
|
|
|
| K4 |
X |
X |
X |
X |
| K5 |
|
|
|
|
| K6 |
|
|
|
|
| K7 |
|
|
|
|
| K8 |
X |
X |
X |
X |
| K9 |
|
|
X |
X |
| K10 |
|
|
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