Subject
Mathematics 1
| 1. | Course Title |
Mathematics 1 Mathematics 1 |
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| 2. | Code | F23L2W002 | ||||||||||||
| 3. | Study Programme | Software Engineering and Information Systems, Internet, Networks and Security, Information Literacy Education, Software engineering and information systems | ||||||||||||
| 4. | Organizer of the study programme (unit, institute, department or division) | Faculty of Computer Science and Engineering | ||||||||||||
| 5. | Degree level (first, second, third cycle) | First Cycle | ||||||||||||
| 6. | Academic year / semester | 1 / Winter | ||||||||||||
| 7. | Number of ECTS credits | 6 | ||||||||||||
| 8. | Teacher | Alexandra Popovska Mitrović, Biljana Toytovska Ribarski, Emil Stankov, Metodija Janceski, Verica Bakeva, Vesna Dimitrievska Ristovska, Vesna Dimitrova | ||||||||||||
| 9. | Prerequisites for enrolling in the course | — | ||||||||||||
| 10. | Objectives of the course programme (competences) | The subject is a support course and is necessary for introducing the concepts of functions, limits, derivatives, and integrals, which are required in almost all upper-level courses. | ||||||||||||
| 11. | Course content | 1. Definition of a function. Properties of functions. Inverse functions. Functions defined piecewise. Operations on functions (addition, subtraction, multiplication, division, and composition). 2. Stretching, compression, translation, and reflection of a function graph. Even and odd functions. Lines (equation of a line through two points, slope). Families of functions (power functions). 3. Polynomials, rational functions, trigonometric functions (definition, period, graph, domain). Inverse functions (domain, range, determining an inverse function, conditions for the existence of an inverse function). 4. Exponential and logarithmic functions (definition, graph, domain, range, exponential and logarithmic growth). Limits (intuitive definition, determination of one-sided and two-sided limits from a function's graph). 5. Infinite limits and limits at infinity. Vertical and horizontal asymptotes. Calculation of limits (basic limits, limits of sums, differences, products, quotients, limits of functions defined by piecewise definitions). 6. Continuity of functions. Limits and continuity of trigonometric functions. 7. Definition of derivative. Tangent. Differentiability. Techniques of differentiation (derivative of a constant, power function, sum, difference, product, quotient). 8. Derivatives of trigonometric functions. Chain rule for the derivative of a composition of functions. Derivatives of exponential and logarithmic functions. Local linear approximation. 9. L'Hospital's rule. Application of derivatives: monotonicity of functions. 10. Application of Derivatives: Convexity and Concavity of Functions, Local Extremums. Investigation of Properties and Sketching the Graph of a Function. 11. Integration (area problem, rectangle method, and antiderivative method). Indefinite integral. Integration by substitution. 12. Definite integral. Fundamental theorem of calculus. Partial integration. Improper integrals (only with infinite limits) |
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| 12. | Learning methods | Lectures using presentations, interactive lectures, exercises (using equipment and software) | ||||||||||||
| 13. | Total available time | 6 ECTS x 30 hours = 180 hours | ||||||||||||
| 14. | Distribution of available time | 45 + 45 + 10 + 0 + 80 = 180 hours | ||||||||||||
| 15. | Forms of teaching activities |
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| 16. | Other forms of activities |
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| 17. | Assessment method |
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| 18. | Grading criteria (points / grade) |
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| 19. | Requirement for obtaining a signature and taking the final exam | — | ||||||||||||
| 20. | Language of instruction | Macedonian | ||||||||||||
| 21. | Method for monitoring the quality of teaching | internal evaluation and survey mechanism | ||||||||||||
| 22. | Literature |
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