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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 | Prof. Dr. Bahadır Özgür Güler, | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | This course aims to analyze real number series; series with positive terms and convergence tests; alternating series; terms of any signed series and convergence tests; power series and their convergence; Taylor series; primitive function and indefinite integral; basic integration methods; The concept of Riemann integral; Some Riemann integrable function classes; Fundamental Theorem of Integral Calculus; Riemann integral calculation techniques; Mean Value Theorems; Applications of definite integral; It is aimed to explain improper integrals and their classification and convergence tests for improper integrals. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | They will learn real number series, series with positive terms and convergence tests, alternating series, series with any signed terms and convergence tests, power series and their convergence, and Taylor series. They will be able to gain the skills to apply them. | 1,3,5,6 | 1, | | LO - 2 : | They will learn the concepts of primitive functions, indefinite integrals, and basic integration methods and gain the skills to apply them. | 1,3,5,6 | 1, | | LO - 3 : | They will learn the concept of Riemann integral, some Riemann integrable function classes, the Fundamental Theorem of Integral Calculus, Riemann integral calculation techniques, Mean Value Theorems, and applications of definite integral and will be able to gain the skills to apply them. | 1,3,5,6 | 1, | | LO - 4 : | They will learn the concept and classification of improper integrals, and convergence tests for improper integrals, and gain the skills to apply them. | 1,3,5,6 | 1, | | LO - 5 : | They will be able to gain the ability to prove simple propositions that are seen as consequences of the fundamental theorems given in the course. | 1,3,5,6 | 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 | | |
| Real number series, series with positive terms and convergence tests, alternating series and convergence tests, series with any signed terms and convergence tests, power series and convergence tests, Taylor series, primitive function and indefinite integral, basic integration methods, concept of Riemann integral, Riemann some classes of integrable functions, fundamental theorem of integral calculus, Riemann integral calculation techniques, mean value theorems, applications of definite integrals, improper integrals and their classification, convergence tests for improper integrals. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Real Number Series, Positive Term Series, and Convergence Tests | | | Week 2 | Alternating Series, Terms Any Signed Series and Convergence Tests
| | | Week 3 | Power Series and Convergences, Taylor Series | | | Week 4 | Primitive Function and Indefinite Integral
| | | Week 5 | Basic Integration Methods | | | Week 6 | Basic Integration Methods | | | Week 7 | Concept of Riemann Integral | | | Week 8 | Some Classes of Riemann Integrable Functions | | | Week 9 | Mid-term exam
| | | Week 10 | Fundamental Theorem of Integral Calculus, Riemann Integral Calculation Techniques | | | Week 11 | Mean Value Theorems
| | | Week 12 | Applications of the Definite Integral | | | Week 13 | Applications of the Definite Integral | | | Week 14 | Improper Integrals and Their Classification | | | Week 15 | Convergence Tests for Improper Integrals | | | Week 16 | End-of-term exam | | | |
| 1 | Sudhir R. Ghorpade, Balmohan V. Limaye, A Course in Calculus and Real Analysis, Springer, New York, 2006. | | | 2 | Binali Musayev, Murat Alp, Nizami Mustafayev, İsmail Ekincioğlu, Teori ve Çözümlü Problemler ile Analiz II, Tekağac Eylül Yayıncılık, Kütahya, 2003. | | | |
| 1 | Edward D. Gaughan, Introduction to Analysis, American Mathematical Society, California, 2009. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 05/04/2025 | 1 | 50 | | End-of-term exam | 16 | 02/06/2025 | 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 | 9 | 14 | 126 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Uygulama | 2 | 14 | 28 | | Dönem sonu sınavı için hazırlık | 16 | 1 | 16 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 240 |
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