| Code: İMÖ 208 |
Course Title: ANALYSIS II |
Theoretical+Practice: 4+2 |
ECTS: 8 |
|
| Year/Semester of Study |
2 / Spring Semester |
| Level of Course |
1st Cycle Degree Programme |
| Type of Course |
Compulsory |
| Department |
ELEMENTARY MATHEMATICS EDUCATION |
| Pre-requisities and Co-requisites |
None |
| Mode of Delivery |
Face to Face |
| Teaching Period |
14 Weeks |
| Name of Lecturer |
ŞENOL KARTAL (senol.kartal@nevsehir.edu.tr) |
| Name of Lecturer(s) |
|
| Language of Instruction |
Turkish |
| Work Placement(s) |
None |
| Objectives of the Course |
| To examine multivariable functions, to interpret the graphs, to be able to interpret the concepts of limit, continuity, part derivative in multiple functions, to make comments about them, to interpret maximum and minimum concepts, to take multi-level integrals and to be able to make applications; To be able to transfer the knowledge acquired in the course to other courses, to create an infrastructure for the course of Differential Equations. |
| Learning Outcomes |
PO |
MME |
| The students who succeeded in this course: |
|
|
| LO-1 |
define multivariable functions and draw graphs |
PO-12 To be able to assess mathematics improvements using different assesment techniques.
|
Examination
|
| LO-2 |
find the limits of two-variable functions by using limit calculation methods |
PO-13 Being capable of using different evaluation and assessment techniques.
|
Examination
|
| LO-3 |
describe the continuity of two variable functions |
PO-18 Using ways to reach the information effectively.
|
Examination
|
| LO-4 |
define derivative of two-variable functions, show derivative calculation methods, define double integrals, use area and volume calculations |
PO-7 To be able to use mathematical language accurately in their mathematics courses and in planning learning and teaching process.
|
Examination
|
| LO-5 |
iki değişkenli fonksiyonların ekstremum değerlerini bularak uygulayabilecek |
PO-6 To be able to design and choose appropriate tools, instruments and materials for mathematics subjects and teaching process.
|
Examination
|
| LO-6 |
take multi-level integrals and apply their applications |
PO-7 To be able to use mathematical language accurately in their mathematics courses and in planning learning and teaching process.
PO-12 To be able to assess mathematics improvements using different assesment techniques.
|
Examination
|
PO: Programme Outcomes
MME:Method of measurement & Evaluation |
| Course Contents |
| The concept of multivariable functions, function definitions and value sets, function drawings. The concept of limit and its applications in two variable functions, the concept of continuity. Partial derivative, chain rule, differential increase and linearization, local extreme values, absolute extreme values and its applications, Lagrange multipliers, the concept of double integral, two-dimensional integrals. |
| Weekly Course Content |
| Week |
Subject |
Learning Activities and Teaching Methods |
| 1 |
The concept of multivariate function, function definition and value sets. |
Lecturing and question solutions |
| 2 |
Function drawings |
Lecturing and question solutions |
| 3 |
The concept of limit and its applications in two variable functions. |
Lecturing and question solutions |
| 4 |
Concept of continuity |
Lecturing and question solutions |
| 5 |
Partial derivative, chain rule, differential increase and linearization in two variable functions. |
Lecturing and question solutions |
| 6 |
Partial derivative, chain rule, differential increase and linearization in two variable functions. |
Lecturing and question solutions |
| 7 |
Local Extremum Values, Absolute Extremum Values and Applications, Lagrange Multipliers |
Lecturing and question solutions |
| 8 |
mid-term exam |
|
| 9 |
Local Extremum Values, Absolute Extremum Values and Applications, Lagrange Multipliers |
Lecturing and question solutions |
| 10 |
Lagrange multipliers. |
Lecturing and question solutions |
| 11 |
The concept of double integral and its calculations. |
Lecturing and question solutions |
| 12 |
The concept of double integral and its calculations. |
Lecturing and question solutions |
| 13 |
Volume calculations in double integrals and other applications. |
Lecturing and question solutions |
| 14 |
Volume calculations in double integrals and other applications. |
Lecturing and question solutions |
| 15 |
Volume calculations in double integrals and other applications. |
Lecturing and question solutions |
| 16 |
final exam |
|
| Recommend Course Book / Supplementary Book/Reading |
| 1 |
• Prof. Dr. Ahmet A. KARADENİZ Yüksek Matematik. Cilt 1, 2. 4. Baskı, 1985. |
| 2 |
• Prof Dr. Mustafa BAYRAKTAR Analize giriş I, II. 2. Baskı, 2008. |
| 3 |
• Prof. Dr. Mustafa BALCI, Analiz 1,2. 7. Baskı, 2008. |
| 4 |
• Doç. Dr. Ahmet TEKCAN, İleri Analiz. DORA 2010. |
| 5 |
• Joel R. Hass, George B. Thomas, Maurice D. Weir, Thomas Calculus I-II, Çeviri Editörü Mustafa Bayram, Pearson Yayıclık, 2010 |
| Required Course instruments and materials |
| Textbooks |
