| Code: İMÖ 305 |
Course Title: ANALYSIS III |
Theoretical+Practice: 3+0 |
ECTS: 5 |
|
| Year/Semester of Study |
3 / Fall 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 |
NERİMAN KARTAL (nerimangok@nevsehir.edu.tr) |
| Name of Lecturer(s) |
|
| Language of Instruction |
Turkish |
| Work Placement(s) |
None |
| Objectives of the Course |
| Defining series concept, positive term series, convergence, divergence, alternating series and power series, measuring series convergence and divergence, examining point and uniform convergence in function series and function series, learning generalized convergence tests, learning Taylor series, learning Fourier series |
| Learning Outcomes |
PO |
MME |
| The students who succeeded in this course: |
|
|
| LO-1 |
To be able to define sequence and series and make applications for them. |
PO-7 To be able to use mathematical language accurately in their mathematics courses and in planning learning and teaching process.
|
Examination
|
| LO-2 |
Be able to determine the series types and determine the convergent and divergent series. |
PO-12 To be able to assess mathematics improvements using different assesment techniques.
|
Examination
|
| LO-3 |
To be able to apply series in daily life |
PO-6 To be able to design and choose appropriate tools, instruments and materials for mathematics subjects and teaching process.
|
Examination
|
| LO-4 |
Be able to determine point and smooth convergence of series. |
PO-1 Having the knowledge of teaching programs, teaching strategies, measurement and assessment methods related to the field
|
Examination
|
| LO-5 |
know alternating series and power series. |
PO-1 Having the knowledge of teaching programs, teaching strategies, measurement and assessment methods related to the field
PO-12 To be able to assess mathematics improvements using different assesment techniques.
|
Examination
|
| LO-6 |
Recognize Taylor series and Fourier series |
PO-12 To be able to assess mathematics improvements using different assesment techniques.
|
Examination
|
PO: Programme Outcomes
MME:Method of measurement & Evaluation |
| Course Contents |
| Sequence concept and applications. Serial concept, positive term series, divergence and convergence in series, alternating series and convergence criteria related to series, power series. Function series, point and uniform convergence in function series, generalized convergence tests, Taylor series and applications in daily life. Fourier series. |
| Weekly Course Content |
| Week |
Subject |
Learning Activities and Teaching Methods |
| 1 |
Sequence concept and applications |
Lecturing and question solutions |
| 2 |
Sequence concept and applications |
Lecturing and question solutions |
| 3 |
Sequence concept and applications |
Lecturing and question solutions |
| 4 |
Series concept and series of positive terms |
Lecturing and question solutions |
| 5 |
Criteria Divergence and convergence and in series. |
Lecturing and question solutions |
| 6 |
Criteria Divergence and convergence and in series. |
Lecturing and question solutions |
| 7 |
Criteria Divergence and convergence and in series. |
Lecturing and question solutions |
| 8 |
mid-term exam |
|
| 9 |
Convergence criteria for alternating series and series. |
Lecturing and question solutions |
| 10 |
Power series |
Lecturing and question solutions |
| 11 |
Series of functions and series expansion |
Lecturing and question solutions |
| 12 |
Generalized convergence series |
Lecturing and question solutions |
| 13 |
Taylor series and applications in daily life |
Lecturing and question solutions |
| 14 |
Fourier series |
Lecturing and question solutions |
| 15 |
Fourier series |
Lecturing and question solutions |
| 16 |
final exam |
|
| Recommend Course Book / Supplementary Book/Reading |
| 1 |
• Joel R. Hass, George B. Thomas, Maurice D. Weir, Thomas Calculus I-II, Çeviri Editörü Mustafa Bayram, Pearson Yayıclık, 2010 |
| 2 |
• Prof. Dr. Ahmet A. KARADENİZ Yüksek Matematik. Cilt 1, 2. 4. Baskı, 1985. |
| 3 |
• Prof Dr. Mustafa BAYRAKTAR Analize giriş I, II. 2. Baskı, 2008. |
| 4 |
• Prof. Dr. Mustafa BALCI, Analiz 1,2. 7. Baskı, 2008. |
| 5 |
• Doç. Dr. Ahmet TEKCAN, İleri Analiz. DORA 2010. |
| Required Course instruments and materials |
| Textbook |
