| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | IMO3012013331 | ANALYSIS III | Compulsory | 3 | 5 | 5 |
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| Level of Course Unit |
| First Cycle |
| Objectives of the Course |
| To teach the concepts of convergence of improper integrals, sequences and series and to gain the ability of using theorems on examples related to these concepts. |
| Name of Lecturer(s) |
| Doç. Dr. Cemal BELEN |
| Learning Outcomes |
| 1 | Learns the concept of improper integral and describes the differences between definite integral. | | 2 | Describes the concept of convergence of sequences and makes related applications. | | 3 | Learns the concept of convergence of series, solves problems by using convergence tests in series. | | 4 | Describes the differences between pointwise and uniform convergence of functional sequences and series. | | 5 | Learns the concepts of power series and Taylor series. |
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| Mode of Delivery |
| Formal Education |
| Prerequisites and co-requisities |
| None |
| Recommended Optional Programme Components |
| None |
| Course Contents |
| Improper integrals,The concept of sequence and its applications, The concept of series,Series with positive terms, Divergence and convergence in series, Alternating series and convergence criterions,, Power series, Functional sequences and series, Pointwise and uniform convergence of functional sequences and series, Generalized convergence tests, Taylor series and its applications, Fourier series.
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| Weekly Detailed Course Contents |
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| 1 | Improper integrals, | | | | 2 | Improper integrals | | | | 3 | The concept of sequence and its applications, | | | | 4 | The concept of series | | | | 5 | Series with positive terms | | | | 6 | Series with positive terms | | | | 7 | Alternating series and convergence criterions,, | | | | 8 | Midterm exam | | | | 9 | Pointwise and uniform convergence of functional sequences and series | | | | 10 | Pointwise and uniform convergence of functional sequences and series | | | | 11 | Power series, | | | | 12 | Power series | | | | 13 | Taylor series and its applications, | | | | 14 | Fourier series | | | | 15 | Fourier series | | | | 16 | Final Exam | | |
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| Recommended or Required Reading |
| 1) Mustafa Balcı (2016). Matematik Analiz Cilt I-II,, Palme Yayınevi , Ankara
2) James Stewart (2016), Calculus, Eight Edition, Boston
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| Planned Learning Activities and Teaching Methods |
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| Assessment Methods and Criteria | |
| SUM | 0 | |
| SUM | 0 | | Yarıyıl (Yıl) İçi Etkinlikleri | 40 | | Yarıyıl (Yıl) Sonu Etkinlikleri | 60 | | SUM | 100 |
| | Language of Instruction | | Turkish | | Work Placement(s) | | None |
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| Workload Calculation |
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| Midterm Examination | 1 | 2 | 2 |
| Final Examination | 1 | 2 | 2 |
| Attending Lectures | 14 | 3 | 42 |
| Problem Solving | 14 | 2 | 28 |
| Individual Study for Homework Problems | 14 | 2 | 28 |
| Individual Study for Mid term Examination | 1 | 24 | 24 |
| Individual Study for Final Examination | 1 | 24 | 24 |
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| Contribution of Learning Outcomes to Programme Outcomes |
| LO1 | 2 | 2 | 2 | 3 | 4 | 3 | 3 | 3 | 4 | 5 | 3 | 4 | 1 | 4 | 5 | 3 | | LO2 | 4 | 5 | 4 | 3 | 3 | 3 | 3 | 5 | 3 | 4 | 3 | 4 | 3 | 4 | 4 | 3 | | LO3 | 3 | 2 | 4 | 5 | 3 | 3 | 3 | 4 | 3 | 2 | 4 | 3 | 3 | 4 | 3 | 2 | | LO4 | 3 | 3 | 4 | 3 | 4 | 5 | 3 | 3 | 2 | 3 | 3 | 4 | 3 | 2 | 2 | 4 | | LO5 | 4 | 2 | 4 | 4 | 3 | 3 | 4 | 4 | 2 | 4 | 4 | 3 | 3 | 3 | 3 | 2 |
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| * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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Ordu University Rectorate Building ,Cumhuriyet Campus , Center / ORDU / TURKEY • Tel: +90 452 226 52 00
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