CALCULUS-I

Course Description

Calculus-I provides the methods of differential and integral calculus with applications in geometry, physics and engineering. Students in this course will learn how to use mathematical language needed for applying the concepts of calculus to numerous applications in science and engineering such as identifying types of functions, graph of functions, evaluating limit of functions, limit of elementary functions (polynomial, trigonometric, logarithmic, exponential,…), methods to solve the undefined limits (L’Hopitals Rule), continuous functions, evaluate derivative of functions, definition of derivative, derivative of elementary functions, derivative of product of two functions and division of functions, applications of derivative, evaluate integrals of functions, definition of the integral, integral of elementary functions, substitution method, integration by parts, integral of rational functions, application of the integral (finding the area) .

CALCULUS-I

Evaluation Tools (Active Term)

Course outcomes

1. 01 Identify types of functions.
2. 02 Calculate limits of functions.
3. 03 Differentiate functions.
4. 04 Draw the graph of a function.
5. 05 Evaluate integrals of functions.
6. 06 Use concepts of limit, derivative and integral in solving fundamental engineering problems.

Course Syllabus

Reference Books & Course Materials

1. 01 Calculus Early Transcendental Functions, Robert T. Smith, Roland B. Mintin, 4th Edition, McGraw-Hill, ISBN 978-0-07-131656-9
2. 02 Thomas' Calculus Early Transcendentals, George B. Thomas, M. D. Weir, J. Hass, F. R. Giordano, 12th Edition , Pearson.
3. 03 Genel matematik 1, Prof dr. İbrahim Ethem Anar, Gazi Kitabevi,2013
4. 04 Analiz 1, Prof. Dr. Mustafa Balcı, Balcı Yayınları.

Learning Outcomes

1. L01 Identify types of functions.
2. L02 Calculate limits of functions.
3. L03 Differentiate functions.
4. L04 Draw the graph of a function.
5. L05 Evaluate integrals of functions.
6. L06 Use concepts of limit, derivative and integral in solving fundamental engineering problems.

Program Outcomes

1. Knowledge of mathematics, natural sciences, basic engineering, computer-based computation, and topics specific to the relevant engineering discipline.
2. Ability to apply knowledge of mathematics, natural sciences, basic engineering, computer-based computation, and topics specific to the relevant engineering discipline to the solution of complex engineering problems.
3. Ability to define complex engineering problems by using knowledge of basic sciences, mathematics, and engineering, while considering the relevant United Nations Sustainable Development Goals (SDGs) related to the problem addressed.
4. Ability to formulate complex engineering problems using knowledge of basic sciences, mathematics, and engineering, while considering the relevant United Nations Sustainable Development Goals (SDGs) associated with the problem addressed.
5. Ability to analyse and solve complex engineering problems using knowledge of basic sciences, mathematics, and engineering, while considering the relevant United Nations Sustainable Development Goals (SDGs) associated with the problem addressed.
6. Ability to design creative solutions to complex engineering problems.
7. Ability to design complex systems, processes, devices, or products in a way that meets present and future needs while considering realistic constraints and conditions.
8. Ability to select and use appropriate techniques and resources—including estimation and modelling—for the analysis and solution of complex engineering problems, while being aware of their limitations.
9. Ability to select and use modern engineering and computational tools—including estimation and modelling—for the analysis and solution of complex engineering problems, while being aware of their limitations.
10. Ability to conduct literature research and use appropriate research methods for the investigation of complex engineering problems.
11. Ability to design experiments for the investigation of complex engineering problems.
12. Ability to conduct experiments, collect data, analyse results, and interpret findings for the investigation of complex engineering problems.
13. Knowledge of the impacts of engineering practices on society, health and safety, the economy, sustainability, and the environment within the framework of the United Nations Sustainable
14. Awareness of the legal implications of engineering solutions within the framework of the United Nations Sustainable Development Goals (SDGs).
15. Knowledge of ethical responsibility and adherence to the principles of professional engineering conduct.
16. Awareness of acting impartially without discrimination in any matter and of being inclusive of diversity.
17. Ability to work effectively as an individual.
18. Ability to work effectively as a team member or leader in intra-disciplinary teams (face-to-face, remote, or hybrid).
19. Ability to work effectively as a team member or leader in multidisciplinary teams (face-to-face, remote, or hybrid).
20. Ability to communicate effectively in spoken form on technical matters, taking into account the diverse characteristics of the target audience (such as education, language, and profession).
21. Ability to communicate effectively in written form on technical matters, taking into account the diverse characteristics of the target audience (such as education, language, and profession).
22. Knowledge of professional practices such as project management and economic feasibility analysis.
23. Awareness of entrepreneurship and innovation.
24. Ability for independent and lifelong learning.
25. Ability to adapt to new and emerging technologies.
26. Lifelong learning ability that includes the capacity to think critically about technological changes.

Po-Lo Matrix