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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 | | İ117B2 | Mathematics I | Compulsory | 1 | 1 | 5 |
| | 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) | | Öğr. Gör. 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 | Apply of the derivative to some engineering problems | | 5 | Know the concepts of integral of functions | | 6 | Apply the integration to some engineering problems and to some applications | | 7 | Can make various applications of arrays and series. | | 8 | Can open functions to Taylor and Maclauren series. |
| | 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 | Trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions | | | | 4 | Limit, rules of limit, continuity | | | | 5 | Derivative of function, geometric meaning of derivative, rules of derivative, derivative of trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions | | | | 6 | Higher order derivative, chain rules, derivative of implicit functions, applications of derivative, concept of differential. | | | | 7 | L’hospital rule, limit at infinity, Rolle Theorem and Mean Value Theorem, extrema of functions | | | | 8 | Midterm | | | | 9 | Asymptotes, plotting graphs by observation of changes in functions. | | | | 10 | Indefinite Integrals | | | | 11 | Integral Computing Methods: Variable Substitution, Partial Integration, Integrals of Polynomial, Algebraic and Trigonometric (Rational) Functions | | | | 12 | Riemann Sums, Certain Integrals and Their Properties, Fundamental Theorem of Analysis | | | | 13 | Variable Transformation in Certain Integrals | | | | 14 | Applications of Certain Integral: Area of Plane Regions, Arc Length, Volume and Surface Areas of Rotary Bodies, Calculation of Mass, Moment, Center of Gravity and Calculation of Work | | | | 15 | Sequences, Series, Alternate Series, Power Series, Series Expansion of Functions, (Taylor and Maclaur's Series) | | |
| | Recommended or Required Reading | | General Mathematics 1, Palme Publishing House, M. Balcı, 2021, 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 | 4 | 56 | | Self Study | 14 | 5 | 70 | | Individual Study for Mid term Examination | 1 | 10 | 10 | | Individual Study for Final Examination | 1 | 11 | 11 | |
| Contribution of Learning Outcomes to Programme Outcomes | | LO1 | 5 | 5 | 4 | 5 | 4 | 5 | 5 | 5 | 4 | 5 | 5 | 4 | 5 | | LO2 | 3 | 2 | 3 | 4 | 5 | 4 | 4 | 5 | 4 | 4 | 4 | 3 | 4 | | LO3 | 5 | 4 | 4 | 4 | 5 | 3 | 3 | 4 | 4 | 4 | 5 | 5 | 3 | | LO4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 5 | 3 | 5 | 3 | 4 | 4 | | LO5 | 4 | 4 | 3 | 3 | 4 | 5 | 4 | 4 | 5 | 5 | 5 | 3 | 4 | | LO6 | 5 | 2 | 3 | 4 | 4 | 3 | 3 | 4 | 4 | 5 | 5 | 4 | 4 | | LO7 | 4 | 5 | 5 | 4 | 4 | 5 | 4 | 4 | 5 | 4 | 3 | 5 | 4 | | LO8 | 4 | 3 | 3 | 3 | 4 | 4 | 5 | 4 | 4 | 4 | 3 | 1 | 3 |
| | * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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