| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | IMO2022013331 | ANALYSIS II | Compulsory | 2 | 4 | 8 |
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| Level of Course Unit |
| First Cycle |
| Objectives of the Course |
| Introduce students to the functions of several variables, provide information about limits, continuity, partial derivatives and applications in two variable functions, double integrals and their applications. |
| Name of Lecturer(s) |
| Doç. Dr. Cemal BELEN |
| Learning Outcomes |
| 1 | Explain the concept of multivariable function. | | 2 | Explain the concepts of limit and continuity of two variable function. | | 3 | Make the calculations of partial derivatives in severable variables | | 4 | Do the applications of derivation in two variable functions. | | 5 | Explain the concept of double integral, calculates the area and volume with the help of double integral, |
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| Mode of Delivery |
| Formal Education |
| Prerequisites and co-requisities |
| None |
| Recommended Optional Programme Components |
| None |
| Course Contents |
| Functions of several variables, limits and continuity in two variable functions, partial derivatives in two variable functions and some applications, double integrals and some applications of double integrals. |
| Weekly Detailed Course Contents |
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| 1 | Topology of R^n | | | | 2 | Functions of sevaral variables, domain and range | | | | 3 | Limits and continuity in two variable functions | | | | 4 | Partial derivatives in two variable functions | | | | 5 | The chain rule, Derivative of implicit functions | | | | 6 | Directional derivatives and gradients | | | | 7 | Tangent planes and differentials | | | | 8 | Midterm exam | | | | 9 | Ekstreme values of functions and saddle points | | | | 10 | Lagrange multipliers method | | | | 11 | Double integrals | | | | 12 | Double integrals in cartesian coordinates | | | | 13 | Changing of variables in double integrals | | | | 14 | Area and volume applications in double integrals | | | | 15 | Final Exam | | |
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| Recommended or Required Reading |
| 1) Mustafa Balcı (2016). Matematik Analiz 2, Palme Yayınevi, Ankara.
2) James Stewart (2016), Calculus, Eight Edition, Boston
3) Mustafa Bayraktar, (2010), Analiz, Nobel Yayınevi, Ankara
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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 | 6 | 84 |
| Problem Solving | 14 | 4 | 56 |
| Individual Study for Homework Problems | 14 | 3 | 42 |
| Individual Study for Mid term Examination | 1 | 27 | 27 |
| Individual Study for Final Examination | 1 | 27 | 27 |
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| Contribution of Learning Outcomes to Programme Outcomes |
| LO1 | 2 | 3 | 4 | 3 | 5 | 4 | 3 | 4 | 5 | 4 | 4 | 5 | 3 | 4 | 5 | 5 | | LO2 | 4 | 3 | 3 | 4 | 4 | 5 | 4 | 4 | 3 | 3 | 4 | 3 | 5 | 4 | 5 | 5 | | LO3 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 5 | 3 | 2 | 2 | 4 | 5 | 3 | 3 | | LO4 | 2 | 3 | 4 | 4 | 5 | 4 | 3 | 2 | 4 | 4 | 4 | 3 | 3 | 3 | 5 | 5 | | LO5 | 4 | 2 | 5 | 4 | 3 | 2 | 4 | 5 | 3 | 3 | 2 | 2 | 3 | 4 | 2 | 5 |
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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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