| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | MAT20220121310 | ANALYSİS IV | Compulsory | 2 | 4 | 7 |
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| Level of Course Unit |
| First Cycle |
| Objectives of the Course |
| The aim of the course is to give convergence theorem for the number and function sequences and series, to examine generalized integral and functions of several variables.
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| Name of Lecturer(s) |
| Prof. Dr. Cemil YAPAR |
| Learning Outcomes |
| 1 | Students who successfully complete this course will develop the right thinking and the ability to interpret and will gain basic knowledge about mathematics. |
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| Mode of Delivery |
| Formal Education |
| Prerequisites and co-requisities |
| The courses, Analysis I, II and III must be achieved |
| Recommended Optional Programme Components |
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| Course Contents |
| Taylor expansion of functions of two variables, maxima and minima, area conversion, vector fields, geometric interpretation of partial derivatives, differentiation under the integral sign. Double integral, transforms the region of double integrals, applications of double integral. Triple integrals, transforms the region of triple integrals, applications of triple integral. Line integrals, Line integrals of scalar fields and vector fields, fundamental theorems of line integrals and Green’s theorem, applications of line integrals. Surface integrals, the first kind of surface integrals, integral on the directed surfaces, fundamental theorems of the surface integrals (Stokes' theorem, Divergence theorem and Gauss's theorem). |
| Weekly Detailed Course Contents |
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| 1 | Taylor expansion of functions of two variables | | | | 2 | Maxima and minima, area conversion | | | | 3 | Vector fields, geometric interpretation of partial derivatives | | | | 4 | Differentiation under the integral sign | | | | 5 | Double integral, transforms the region of double integrals, applications of double integral | | | | 6 | Triple integrals, transforms the region of triple integrals, applications of triple integral | | | | 7 | Line integrals | | | | 8 | Midterm exam | | | | 9 | Line integrals of scalar fields and vector fields, the convergence criteria for integrals | | | | 10 | Fundamental theorems of line integrals and Green’s theorem | | | | 11 | Applications of line integrals | | | | 12 | Surface integrals | | | | 13 | The first kind of surface integrals | | | | 14 | Integral on the directed surfaces | | | | 15 | Fundamental theorems of the surface integrals (Stokes' theorem, Divergence theorem and Gauss's theorem). | | | | 16 | Final exam | | |
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| Recommended or Required Reading |
| Analiz II, Mustafa BALCI
Yüksek Matematik Cilt II, Ahmet KARADENİZ
Yüksek Matematik Cilt II, Hüseyin HALİLOV
Ömer AKIN, Matematik Analiz ve Analitik Geometri (cilt 1-2), Palme Yayıncılık, 2001
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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 | 1.5 | 1.5 |
| Final Examination | 1 | 1.5 | 1.5 |
| Attending Lectures | 14 | 6 | 84 |
| Self Study | 14 | 4 | 56 |
| Individual Study for Homework Problems | 14 | 2.5 | 35 |
| Individual Study for Mid term Examination | 2 | 6 | 12 |
| Individual Study for Final Examination | 3 | 8 | 24 |
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| Contribution of Learning Outcomes to Programme Outcomes |
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| * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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