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| MAT2014 | Analysis - IV | 4+2+0 | ECTS:7 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures and 2 hours of practicals per week | | Lecturer | Prof. Dr. Mehmet AKBAŞ | | Co-Lecturer | DOCTOR LECTURER Meltem SERTBAŞ, | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of the course is to give students integration over a subset of n-dimensional Euclidean space and vector calculus. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | apply the concepts to solve problems in high dimensional analysis. | 3,5,6,7 | 1 | | LO - 2 : | consolidate one dimensional Analysis concepts well. | 3,5,6,7 | 1 | | LO - 3 : | solve maximum and minumum problems in high dimensional Analysis. | 3,5,6,7 | 1 | | LO - 4 : | learn the integral concepts in high dimensional Analysis. | 3,5,6,7 | 1 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| Multiple integrals. Application of double and triple integrals. Change of variables for double and triple integrals. Integral and uniform convergence. Vectoral analysis. Gradient, Rotation, Divergence. Integrals along paths. Surfaces and surface integrals. Green theorem, Divergence theorem, Stokes theorem |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Maximum and minumum, critical points, Taylor expansions, second derivative test | | | Week 2 | Maximum and minumum problems with constraints, Lagrange multiplier rule | | | Week 3 | Extremum points over closed sets and solutions of related problems | | | Week 4 | Integral over n-dimensional rectangles, definitions
| | | Week 5 | Multiple integrals as iterated integrals | | | Week 6 | Integral over more general sets
| | | Week 7 | Evaluation of multiple integrals and solutions of problems | | | Week 8 | Mid-term exam | | | Week 9 | Integration and uniform convergence | | | Week 10 | Vectors, vector product, gradient, divergence, curl | | | Week 11 | Paths and curves, parametric equations, reparametrization
| | | Week 12 | Integrals along paths, surfaces, surface integrals | | | Week 13 | Integral theorems, Green theorem, orientations | | | Week 14 | Gauss's divergence theorem, Stokes's theorem and solutions of problems
| | | Week 15 | Orientable and non-orientable surfaces | | | Week 16 | End-of-term exam | | | |
| 1 | Webb, J.R.L. 1991; Functions of Several Real Variables, Ellis Horwood Limited, England | | | |
| 1 | Fleming, W.H. 1977; Functions of Several Variables, Springer, 2nd Ed., New York | | | 2 | Spivak, M. 1967; Calculus, W. A. Benjamin Inc., ABD | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 10/04/2018 | 2 | 50 | | End-of-term exam | 16 | 30/05/2018 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 14 | 56 | | Sınıf dışı çalışma | 6 | 14 | 84 | | Arasınav için hazırlık | 1 | 8 | 8 | | Arasınav | 2 | 1 | 2 | | Uygulama | 2 | 14 | 28 | | Dönem sonu sınavı için hazırlık | 3 | 10 | 30 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 210 |
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