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| MAT1006 | Analysis - II | 4+2+0 | ECTS:8 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures and 2 hours of practicals per week | | Lecturer | Prof. Dr. Mehmet KUNT | | Co-Lecturer | Doç. DR. Ali Hikmet DEĞER, | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of this course is to teach basic mathematical techniques. To introduce the mathematical skills necessary to analyze engineering problems in 2 and especially 3-dimensional space. Emphasis is placed on the practical usability of mathematics with a large number of sample problems. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | Can make various applications of integral and apply it to engineering problems | 1,3,5,7 | 1,3,6 | | LO - 2 : | Can perform convergence analysis of generalized integrals | 1,3,5,7 | 1,3,6 | | LO - 3 : | Know the concept of Can analyze the convergence of sequences and series | 1,3,5,7 | 1,3,6 | | LO - 4 : | Comprehend the functions and properties of multivariables | 1,3,5,7 | 1,3,6 | | LO - 5 : | Know the concept of limit and continuity in multivariable functions | 1,3,5,7 | 1,3,6 | | LO - 6 : | Know the concept of derivative in multivariable functions, apply it to engineering problems | 1,3,5,7 | 1,3,6 | | LO - 7 : | Know the concept of integral in multivariable functions and apply it to engineering problems | 1,3,5,7 | 1,3,6 | | 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 | | |
| Riemann sums, definite integrals and their properties, fundamental theorem of integral calculus. Variable transformation in definite integrals and areas between curves Applications of definite integrals: Calculation of volume (disk, flake and shell method), Arc length, areas of rotating surfaces. Generalized Integral (1st and 2nd Type) Sequences and Infinite Series (Convergence and Divergence concept, geometric series, divergence test, integral test, comparison, ratio and root test). Alternate series, absolute and conditional convergence, power series, Taylor and Maclaurin series. Multivariable functions, the concept of limits and continuity and partial derivatives. Chain rule, directional derivatives and gradients. Extreme values, absolute maximum and absolute minimum, Lagrange multipliers (Single conditional). Double integrals and their applications ( Area). Variable transformation in multiple integrals, polar coordinates and double integral in polar coordinates and its applications (Mass and density, center of mass). |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 |
Riemann sums, definite integrals, and their properties, fundamental theorem of integral calculus | | | Week 2 | Variable transformation in definite integrals and areas between curves
| | | Week 3 | Applications of definite integral: Calculation of volume (Disc, flake and shell method) | | | Week 4 | Arc length of parametric curves, areas of rotational surfaces
| | | Week 5 | Generalized integrals(types 1 and 2) | | | Week 6 | Sequences and Infinite Series(Convergence and Divergence concept, geometric series, nth term test, integral test, comparison, ratio and root test) | | | Week 7 | Alternating series, absolute and conditional convergence, power series | | | Week 8 | Taylor and Maclaurin series | | | Week 9 | Mid-term exam
| | | Week 10 | Multivariable functions, the concept of limits and continuity and partial derivatives | | | Week 11 | Chain rule, directional derivatives and gradient vectors
| | | Week 12 | Extreme values, absolute maximum and absolute minimum, Lagrange multipliers (Single conditional) | | | Week 13 | Double integrals and their applications (Area)
| | | Week 14 | Variable transformation in multiple integrals, polar coordinates and polar curves,
Double integral in polar coordinates and its applications (Mass and density, center of mass) | | | Week 15 | General evaluation | | | Week 16 | End-of-term exam | | | |
| 1 | Thomas, G.B., Finney, R.L.. (Çev: Korkmaz, R.), 2001. Calculus ve Analitik Geometri, Cilt I-II, Beta Yayınları, İstanbul. | | | |
| 1 | Balcı, M. 2009. Genel Matematik 1-2, Balcı Yayınları, Ankara. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 05/04/2022 | 1 | 50 | | End-of-term exam | 16 | 02/06/2022 | 1 | 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 | 8 | 14 | 112 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Uygulama | 2 | 14 | 28 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 10 | 1 | 10 | | Proje | 0 | 0 | 0 | | Kısa sınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 12 | 1 | 12 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 234 |
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