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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 | | ELM106B | Mathematics II | Compulsory | 1 | 2 | 4 |
| | Level of Course Unit | | First Cycle | | Objectives of the Course | | It aims to teach students basic mathematical techniques, introduce the mathematical skills necessary to analyze problems, and emphasize the practical use of mathematics with numerous sample problems. | | Name of Lecturer(s) | | Dr. Öğr. Üyesi Aykut COŞKUN | | 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 | Know the concepts of limit continuity and derivative of functions of two and three variables apply it to engineering problems | | 5 | Applies surface integral to engineering problems. |
| | Mode of Delivery | | Normal Education | | Prerequisites and co-requisities | | None | | Recommended Optional Programme Components | | None | | Course Contents | | Matrix, canonical form of the matrices, eigenvalues and eigenvectors, determinant, inverse matrices, linear system of equations and solutions. 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 | Linear Equation Systems and Solution with the Help of Echelon Form and Crammer Method. | | | | 3 | Conic Sections and Quadratic Equations, Polar Coordinates and Graph Drawings, Parametrization of Curves in the Plane | | | | 4 | Three-Dimensional Space and Cartesian Coordinates, Vectors in the Plane and Space, Point, Vector and Mixed Products | | | | 5 | Lines and Planes, Cylinders, Cones and Sphere, Cylindrical and Spherical Coordinates in Three-Dimensional Space | | | | 6 | Vector Valued Functions and Curves in Space, Curvature, Torsion and TNB Frame. | | | | 7 | Multivariable Functions, Limit, Continuity and Partial Derivatives | | | | 8 | Midterm exam | | | | 9 | Chain Rule, Direction Derivatives, Gradient, Divergence, Rotational, and Tangent Planes | | | | 10 | Extreme Values and Saddle Points, Lagrange Multipliers, Taylor and Maclaurin Series | | | | 11 | Twofold Integrals, Area, Moment and Center of Gravity, Twofold Integrals in Polar Form, Threefold Integrals in Cartesian Coordinates | | | | 12 | Mass, Moment and Center of Gravity in Three-Dimensional Space, Threefold Integrals in Cylindrical and Spherical Coordinates, Variable Transformation in Multifold Integrals. | | | | 13 | Curvilinear Integrals, Vector Fields, Work, Flux, Green's Theorem in the Plane. | | | | 14 | Surface Area and Surface Integrals, Stokes Theorem, Divergence Theorem and Applications | | | | 15 | General Repetition and Example Solutions | | |
| | Recommended or Required Reading | | Thomas, G.B. ve Finney, R.L.. (Çev: Korkmaz, R.), 2001; Calculus ve Analitik Geometri, Cilt I, Beta Yayınları, İstanbul.
Balcı, M. 2009; Genel Matematik 2, Balcı Yayınları, Ankara.
Kolman, B. ve Hill, D.L., Çev Edit: Akın, Ö. 2002 ; Uygulamalı Lineer Cebir, Palme Yayıncılık, Ankara. | | Planned Learning Activities and Teaching Methods | | | Assessment Methods and Criteria | |
| Midterm Examination | 1 | 100 | | SUM | 100 | |
| Final Examination | 1 | 100 | | SUM | 100 | | Term (or Year) Learning Activities | 40 | | End Of Term (or Year) Learning Activities | 60 | | SUM | 100 |
| | Language of Instruction | | Turkish | | Work Placement(s) | | None |
| | Workload Calculation | |
| Midterm Examination | 1 | 1 | 1 | | Final Examination | 1 | 2 | 2 | | Attending Lectures | 14 | 1 | 14 | | Self Study | 14 | 2 | 28 | | Individual Study for Mid term Examination | 8 | 4 | 32 | | Individual Study for Final Examination | 8 | 4 | 32 | |
| Contribution of Learning Outcomes to Programme Outcomes | | LO1 | 2 | 1 | 1 | 1 | 2 | 2 | | LO2 | 2 | 1 | 1 | 1 | 2 | 2 | | LO3 | 2 | 1 | 1 | 1 | 3 | 2 | | LO4 | 3 | 1 | 1 | 1 | 3 | 3 | | LO5 | 2 | 1 | 1 | 1 | 2 | 2 |
| | * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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