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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 | | ELM105B | Mathematics I | Compulsory | 1 | 1 | 4 |
| | Level of Course Unit | | First Cycle | | Objectives 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. | | Name of Lecturer(s) | | Dr. Öğr. Üyesi Ramazan ŞİMŞEK | | Learning Outcomes | | 1 | Clasify numbers and understand functions and their properties | | 2 | Know the concepts of limit and continuity of functions | | 3 | Know the concepts of derivatives of functions | | 4 | Can make various applications of derivatives and apply them to engineering problems | | 5 | Know the concepts of integral of functions | | 6 | Apply the integration to some engineering problems and to some applications |
| | Mode of Delivery | | Normal Education | | Prerequisites and co-requisities | | None | | Recommended Optional Programme Components | | None | | Course Contents | | 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. Change of variables for definite integrals. Applications of definite integrals: areas of regions, length of curves, volumes of rotating objects, surface arease, calculation of mass, moment, gravitational center and work. Generalization of integration. Sequences, series, alternating series, power series, series expansion of functions (Taylor and Maclaurin series). | | Weekly Detailed Course Contents | |
| 1 | Functions, inverse functions, plotting the graphs of basic curves, transformation of graphs | | | | 2 | Trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions | | | | 3 | Limit, rules of limit, continuity | | | | 4 | Derivative of function, geometric meaning of derivative, rules of derivative, derivative of trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions | | | | 5 | Higher order derivative, chain rules, derivative of implicit functions, applications of derivative, concept of differential. | | | | 6 | L’hospital rule, limit at infinity, Rolle Theorem and Mean Value Theorem, extrema of functions | | | | 7 | Asymptotes, plotting graphs by observation of changes in functions. | | | | 8 | Midterm exam | | | | 9 | Indefinite Integrals | | | | 10 | Integral Calculation Methods: Variable Substitution, Partial Integration, Integrals of Polynomial, Algebraic and Trigonometric (Rational) Functions | | | | 11 | Riemann Sums, Definite Integrals and Their Properties, Fundamental Theorem of Calculus | | | | 12 | Applications of definite integrals: areas of regions, length of curves, volumes of rotating objects, surface arease, calculation of mass, moment, gravitational center and work. | | | | 13 | Applications of Definite Integral: Area of Planar Regions, Arc Length, Volume and Surface Areas of Rotational Bodies, Mass Calculation, Moment, Center of Gravity and Work Calculation | | | | 14 | Sequences, series, alternating series, power series, series expansion of functions (Taylor and Maclaurin series) | | | | 15 | General Repetition and Example Solutions | | |
| | Recommended or Required Reading | | Balcı, M. 2009;Genel Matematik 1, Balcı Yayınları, Ankara.
Thomas, G.B. ve Finney, R.L.. (Çev: Korkmaz, R.), 2001; Calculus ve Analitik Geometri, Cilt I, Beta Yayınları, İstanbul. | | 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 | | Individual Study for Mid term Examination | 10 | 4 | 40 | | Individual Study for Final Examination | 12 | 4 | 48 | |
| Contribution of Learning Outcomes to Programme Outcomes | | LO1 | 3 | 1 | 1 | 1 | 2 | 2 | | LO2 | 2 | 1 | 1 | 1 | 3 | 2 | | LO3 | 3 | 1 | 1 | 1 | 2 | 2 | | LO4 | 3 | 1 | 1 | 1 | 3 | 2 | | LO5 | 2 | 1 | 1 | 1 | 2 | 2 | | LO6 | 4 | 1 | 1 | 1 | 3 | 2 |
| | * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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