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| MAT 117 | Mathematics - I | 4+0+0 | ECTS:6 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of MECHANICAL ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | -- | | Co-Lecturer | Lecturers | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of the course is to teach the basic mathematical techniques, introducing at the same time a number of mathematical skills which can be used for the analysis of problems. The emphasis is on the practical usability of mathematics; this goal is mainly pursued via a large variety of examples and applications from these disciplines. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | clasify numbers and understand functions and their properties | 1,3 | 1 | | LO - 2 : | know the concepts of limit and continuity of functions | 2,3 | 1 | | LO - 3 : | know the concepts of derivatives of functions | 2,3 | 1 | | LO - 4 : | apply of the derivative to some engineering problems | 3,4,5 | 1 | | LO - 5 : | know the concepts of integral of functions | 3,4,5 | 1 | | LO - 6 : | apply the integration to some engineering problems and to some applications | 3,4,5 | 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 | | |
| Functions, inverse functions, plotting the graphs of basic curves, transformation of graphs. Trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions . Limit, rules of limit, continuity . Derivative of function, geometric meaning of derivative, rules of derivative, derivative of trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions. Higher order derivative, chain rules, derivative of implicit functions, applications of derivative, concept of derivation. L' hospital rule, limit at infinity, Rolle Theorem and Mean Value Theorem, extrema of functions . Asymptotes, plotting graphs by observation of changes in functions . Indefinite integrals . Methods of integration, change of variable, integration by parts, integration of polynomials, algebraic and trigonometric (rational) functions . Riemann sums, definite integration and properties, fundamental theorem of analysis. Applications of definite integrals: areas of regions, length of curves, volumes of rotating objects, surface arease, calculation of mass, moment, gravitational center and work. Change of variables for definite integrals. Generalization of integration . Sequences, series, alternating series, power series, series expansion of functions (Taylor and Maclaurin series)
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Functions, inverse functions, plotting the graphs of basic curves, transformation of graphs. | | | Week 2 | Trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions. | | | Week 3 | Limit, rules of limit, continuity. | | | Week 4 | Derivative of function, geometric meaning of derivative, rules of derivative, derivative of trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions | | | Week 5 | Higher order derivative, chain rules, derivative of implicit functions, applications of derivative, concept of derivation. | | | Week 6 | L'hospital rule, limit at infinity, Rolle Theorem and Mean Value Theorem, extrema of functions. | | | Week 7 | Asymptotes, plotting graphs by observation of changes in functions | | | Week 8 | Indefinite integrals | | | Week 9 | Mid-term exam | | | Week 10 | Methods of integration, change of variable, integration by parts, integration of polynomials, algebraic and trigonometric (rational) functions | | | Week 11 | Riemann sums, definite integration and properties, fundamental theorem of analysis | | | Week 12 | Change of variables for definite integrals. | | | Week 13 | Applications of definite integrals: areas of regions, length of curves, volumes of rotating objects, surface arease, calculation of mass, moment, gravitational center and work. | | | Week 14 | Generalization of integration | | | Week 15 | Sequences, series, alternating series, power series, series expansion of functions (Taylor and Maclaurin series) | | | Week 16 | End-of-term exam | | | |
| 1 | Thomas, G.B., Finney, R.L.. (Çev: Korkmaz, R.), 2001. Calculus ve Analitik Geometri, Cilt I, Beta Yayınları, İstanbul. | | | |
| 1 | Balcı, M. 2009. Genel Matematik 1, Balcı Yayınları, Ankara | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 22-11-2013 | 2 | 50 | | End-of-term exam | 16 | 16-01-2014 | 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 | 5 | 14 | 70 | | Arasınav için hazırlık | 9 | 1 | 9 | | Arasınav | 15 | 1 | 15 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 162 |
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