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Description of Individual Course Units| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | DUM2022022252 | | Compulsory | 2 | 4 | 3 |
| | Level of Course Unit | | First Cycle | | Objectives of the Course | | The aim of the course is to teach the basic mathematical techniques. Analyzing the two and three dimensional problems in engineering sciences and introducing 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. | | Name of Lecturer(s) | | | Learning Outcomes | | 1 | It is the acquisition of basic knowledge in mathematics. | | 2 | Knows the concepts of conic sections and express in polar coordinates. | | 3 | Knows vectors in two and three dimensional spaces |
| | Mode of Delivery | | Formal Education | | Prerequisites and co-requisities | | | Recommended Optional Programme Components | | | Course Contents | | Indefinite integrals, integration techniques • Definite integrals, the upper and lower Darboux sums and integral of staircase functions • Riemann integrals, Riemann integrable function in terms of classes • The fundamantal theorems of integral calculus • Account with the help of the definite integral of some special limits • Domain as the application of definite integral • Arc length, calculating of volume and areas of surfaces of revolution • Infinite series, convergence and divergence of the series • Positive series and convergence criteria • Alternating series • Absolute and conditional convergence • Any polynomial series and Abel partial sum • Convergence of infinite products and related criteria | | Weekly Detailed Course Contents | |
| 1 | Indefinite integrals, integration techniques | | | | 2 | Definite integrals, the upper and lower Darboux sums and integral of staircase functions | | | | 3 | Riemann integrals, Riemann integrable function in terms of classes | | | | 4 | The fundamantal theorems of integral calculus | | | | 5 | Account with the help of the definite integral of some special limits | | | | 6 | Domain as the application of definite integral | | | | 7 | Arc length, calculating of volume and areas of surfaces of revolution | | | | 8 | Mid-term exam | | | | 9 | Chain rule, directional derivative, gradient, divergence, rotational and tangent planes. | | | | 10 | Ekstremum values and saddle points, Lagrange multipliers, Taylor and Maclaurin series. | | | | 11 | Double integration, areas, moment and gravitational center. Double integrals in polar coordinates. Triple integrals in cartesian coordinates. | | | | 12 | Mass, moment and gravitational center in three dimensional space. Triple integrals in cylindrical and spherical coordinates. Change of variables in multiple integrals. | | | | 13 | Line integrals, vector fields, work, flux. Green’s theorem on plane. | | | | 14 | Areas of surface and surface integrals. | | | | 15 | Final exam | | |
| | Recommended or Required Reading | | Thomas, G.B., Finney, R.L.. (Çev: Korkmaz, R.), 2001. Calculus ve Analitik Geometri, Cilt II, Beta Yayınları, İstanbul. Balcı, M. 2009. Genel Matematik 2, Balcı Yayınları, Ankara Kolman, B., Hill, D.L. (Çev Edit: Akın, Ö.) 2002. Uygulamalı lineer cebir. Palme Yayıncılık, Ankara. | | Planned Learning Activities and Teaching Methods | | | Assessment Methods and Criteria | |
| SUM | 0 | |
| SUM | 0 | | Yarıyıl (Yıl) İçi Etkinlikleri | 40 | | Yarıyıl (Yıl) Sonu Etkinlikleri | 60 | | SUM | 100 |
| | Language of Instruction | | Turkish | | Work Placement(s) | |
| | Workload Calculation | |
| Midterm Examination | 1 | 1 | 1 | | Final Examination | 1 | 1 | 1 | | Attending Lectures | 14 | 4 | 56 | | Self Study | 5 | 2 | 10 | | Individual Study for Mid term Examination | 2 | 2 | 4 | | Individual Study for Final Examination | 2 | 3 | 6 | |
| Contribution of Learning Outcomes to Programme Outcomes | | LO1 | 5 | 4 | 3 | 5 | 3 | 4 | 4 | 3 | 5 | 4 | 3 | 4 | | LO2 | 5 | 5 | 4 | 3 | 3 | 5 | 4 | 4 | 4 | 4 | 3 | 2 | | LO3 | 5 | 4 | 4 | 4 | 2 | 4 | 5 | 3 | 5 | 4 | 3 | 2 |
| | * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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