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| MAT1011 | Mathematics - I | 4+0+0 | ECTS:5 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of METALLURGICAL and MATERIALS ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Dr. Öğr. Üyesi Seda ÖZTÜRK | | Co-Lecturer | Other instructor assigned for the course | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course aims to provide the basic information about functions, limit, derivative, integral as well as their appicaitons in various disciplines including physical and engineering sciences. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | learn how to model with functions | 1,2 | 1 | | LO - 2 : | learn about limit, derivative and applications | 1,2 | 1 | | LO - 3 : | learn about integral and their applications | 1,2 | 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 (polynomials, rational, trigonometric, hyperbolic, exponential, logarithmic and inverse trigonometric functions) graphs of basic functions, shifting and scaling graphs, limit, continuity, differentiation and applications (Intermediate Value Theorem, L'hopital's rule, Mean Value Theorem, Optimization problems, sketching the graph of a function), integration techniques |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Real numbers and the real line, Cartesian coordinates in the plane, graphs of second-degree equations, functions and the graphs of simple functions. | | | Week 2 | Addition, subtraction, multiplication, division, and composition of functions, composite and piecewise functions, polynomials and rational functions, trigonometric functions. | | | Week 3 | Trigonometric functions, limit with examples of speed, growth rate, and area, limits of functions, limits at infinity and infinite limits. | | | Week 4 | Continuity, continuous functions on closed, finite intervals, tangent lines and slopes, derivative and rules of differentiation. | | | Week 5 | Derivative and rules of differentiation, chain rule, derivatives of trigonometric functions, higher-order derivatives. | | | Week 6 | Mean value theorem, increasing/decreasing functions, derivative of closed functions, inverse functions.
| | | Week 7 | Exponential and logarithmic functions, natural logarithm and exponential functions, inverse trigonometric functions, hyperbolic functions. | | | Week 8 | Related rates, indeterminate forms, L'Hôpital's rule, extrema values. | | | Week 9 | Midterm exam | | | Week 10 | Concavity and inflections, graphing functions, optimization problems.
| | | Week 11 | Sums and sigma notation, areas with limits of sums, definite integral, properties of definite integrals. | | | Week 12 | Fundamental theorem of calculus, substitution (change of variables) method, integration by parts method. | | | Week 13 | Integrals of rational functions, integral calculation using inverse trigonometric substitution, integral calculation using the half-angle method (tan(??/2) substitution).
| | | Week 14 | First/second type improper integrals, p-integrals, comparison test for improper integrals, applications of integrals (area and volume calculation). | | | Week 15 | Applications of integrals (area and volume calculation), applications of integrals (arc length and surface area). | | | Week 16 | Final exam | | | |
| 1 | Zill, D.G, Wright, W.S., 2012; Matematik Cilt I (Calculus Early Transcendentals), Çeviri Editörü Prof. Dr. İsmail Naci Cangül, Nobel Yayıncılık, Ankara. | | | |
| 1 | Thomas, G.B., Weir, M.D., Hass, J., 2009; Thomas' Calculus, 12th Edition, Pearson, USA. | | | 2 | Adams, R.A., Essex, C., Calculus a Complete Course, 2012, Pearson, USA. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 28.11.2023 | | 50 | | End-of-term exam | 16 | 22.01.2024 | | 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 | 12 | 1 | 12 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 15 | 1 | 15 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 157 |
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