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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 | | DUİM1022016252 | MATHEMATICS II | Compulsory | 1 | 2 | 4 |
| | 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 sciencies 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 | knows the concepts of matrix and determinant and enable to solve system of equations | | 2 | knows the concepts of conic sections and express in polar coordinates. | | 3 | know vectors in two and three dimensional spaces | | 4 | understand functions of two and three variables and their properties | | 5 | know the concepts of limit and continuity of functions of two and three variables | | 6 | know the concepts of derivative and apply it to engineering problems | | 7 | know the concepts of integration and apply it to engineering problems |
| | Mode of Delivery | | Formal Education | | Prerequisites and co-requisities | | None | | Recommended Optional Programme Components | | None | | Course Contents | | Matrices, determinants, eigenvalues and eigenvectors, inverse matrix. Systems of lineer equations and solutions by reduction to echelon form and Crammer rule. Conic sections and quadratic equations, polar coordinates and plotting graphs, parameterization of curves on plane. Three dimensional space and Cartesian coordinates. Vectors on the plane and space. Dot, cross and scalar triple product. Lines and planes on three dimensional space. Cylinders, conics and sphere. Cylindrical and spherical coordinates. Vector valued functions, and curves on the space, curvature, torsion and TNB frame. Multi variable functions, limit, continuity and partial derivative. Chain rule, directional derivative, gradient, divergence, rotational and tangent planes. Ekstremum values and saddle points, Lagrange multipliers, Taylor and Maclaurin series. Double integration, areas, moment and gravitational center. Double integrals in polar coordinates. Triple integrals in cartesian coordinates. Mass, moment and gravitational center in three dimensional space. Triple integrals in cylindrical and spherical coordinates. Change of variables in multiple integrals. Line integrals, vector fields, work, flux. Green's theorem on plane. Areas of surface and surface integrals. Stokes theorem, divergence theorem and applications. | | Weekly Detailed Course Contents | |
| 1 | Matrices, determinants, eigenvalues and eigenvectors, inverse matrix.
| | | | 2 | Systems of lineer equations and solutions by reduction to echelon form and Crammer rule | | | | 3 | Conic sections and quadratic equations, polar coordinates and plotting graphs, parameterization of curves on plane. | | | | 4 | Three dimensional space and Cartesian coordinates. Vectors on the plane and space. Dot, cross and scalar triple product. | | | | 5 | Lines and planes on three dimensional space. Cylinders, conics and sphere. Cylindrical and spherical coordinates. | | | | 6 | Vector valued functions, and curves on the space, curvature, torsion and TNB frame. | | | | 7 | Multi variable functions, limit, continuity and partial derivative. | | | | 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 | Stokes theorem, divergence theorem and applications. | | | | 16 | End-of-term 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) | | None |
| | Workload Calculation | |
| Midterm Examination | 1 | 2 | 2 | | Final Examination | 1 | 2 | 2 | | Attending Lectures | 14 | 3 | 42 | | Self Study | 5 | 5 | 25 | | Individual Study for Mid term Examination | 5 | 4 | 20 | | Individual Study for Final Examination | 5 | 4 | 20 | |
| Contribution of Learning Outcomes to Programme Outcomes | | LO1 | 5 | 2 | 2 | 5 | 1 | 1 | 2 | 2 | 2 | 1 | 3 | 2 | | LO2 | 5 | 2 | 2 | 5 | 2 | 2 | 3 | 3 | 2 | 3 | 3 | 2 | | LO3 | 5 | 3 | 3 | 5 | 2 | 3 | 3 | 3 | 2 | 2 | 4 | 2 | | LO4 | 2 | 1 | 1 | 2 | 5 | 1 | 1 | 2 | 2 | 1 | 5 | 1 | | LO5 | 2 | 2 | 2 | 1 | 5 | 2 | 3 | 3 | 2 | 2 | 5 | 3 | | LO6 | 3 | 2 | 2 | 2 | 5 | 1 | 1 | 2 | 2 | 2 | 5 | 2 | | LO7 | 1 | 2 | 2 | 2 | 5 | 2 | 1 | 2 | 2 | 2 | 5 | 2 |
| | * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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