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| MAT1005 | Analysis - I | 4+2+0 | ECTS:9 | | Year / Semester | Fall 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: | | It is aimed at sets and real numbers systems; basic algebraic inequalities and the Mathematical Induction Method; concepts of relations and functions (trigonometric, exponential, logarithmic, and hyperbolic functions); real number sequences and their convergence; The basic properties of convergent sequences are; lower and upper limits of real number sequences; limits and continuity of functions; Basic properties of continuous functions; explain the concept of derivative, the basic properties of differentiable functions and the applications of derivative. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | They will learn the sets and real number system, basic algebraic inequalities, and the Mathematics Induction Method, and gain the skills to apply them. | 1,3,5,6 | 1, | | LO - 2 : | They will learn the concepts of relations and functions, trigonometric, exponential, logarithmic, and hyperbolic functions, and gain the skills to apply them. | 1,3,5,6 | 1, | | LO - 3 : | They will learn the concepts of real number sequences and convergence, the basic properties of convergent sequences, lower and upper limits of real number sequences and gain the skills to apply them. | 1,3,5,6 | 1, | | LO - 4 : | They will be able to see the similarities and differences between the concepts of limit, continuity, and differentiability in real-valued functions 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 | | |
| Sets and elementary operations on sets, real number system and principles, basic algebraic inequalities and mathematical induction method, relations and functions, trigonometric, exponential, logarithmic, and hyperbolic functions, real number sequences and convergence, basic properties of convergent sequences, substructure and functions of real number sequences. upper limits, limits of functions, continuity of functions, basic properties of continuous functions, basic properties of derivative and differentiable functions, and applications of derivatives. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Sets and Elementary Operations on Sets | | | Week 2 | Real Number System and Principles | | | Week 3 | Basic Algebraic Inequalities and the Mathematics Induction Method | | | Week 4 | Correlations and Functions | | | Week 5 | Trigonometric, Exponential, Logarithmic and Hyperbolic Functions | | | Week 6 | Real Number Sequences and Convergence | | | Week 7 | Basic Properties of Convergent Sequences | | | Week 8 | Lower and Upper Limits of Real Number Sequences | | | Week 9 | Mid-term exam | | | Week 10 | Limits of Functions | | | Week 11 | Continuities of Functions | | | Week 12 | Basic Properties of Continuous Functions | | | Week 13 | Basic Properties of Derivative and Differentiable Functions | | | Week 14 | Applications of Derivative | | | Week 15 | Applications of Derivative | | | 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 I, 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 | 28/11/2024 | 2 | 50 | | End-of-term exam | 16 | 15/01/2025 | 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 | 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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