### Calculus I (MATH 101)

2023 Spring
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
5/6 ECTS (for students admitted in the 2013-14 Academic Year or following years)
Nilay Duruk Mutlubaş nilaydm@sabanciuniv.edu, Matteo Paganin paganin@sabanciuniv.edu,
English
--
Interactive,Learner centered,Communicative,Discussion based learning,Guided discovery

### CONTENT

Basic functions; their properties and applications to modeling. Rate of change, limit, derivative and linear approximation. Computational techniques. Local and global extrema. Applications to optimization problems. The definite integral. Antiderivatives and the Fundamental Theorem of Calculus. Integration techniques. Improper integrals. Applications.

### OBJECTIVE

To teach fundamental notions of calculus in single variable.

### LEARNING OUTCOMES

• Understand and use basic properties of elementary functions
• Understand the idea of limit analytically/graphically, and evaluate limits
• Understand the definition of derivative and its geometric meaning
• Compute derivatives using standard differentiation techniques
• Apply the notion of derivative graphing and optimization problems
• Understand the definition of definite integral and its geometric meaning
• Compute integrals using standard integration techniques
• Understand the idea of integration over unbounded intervals and compute them

### PROGRAMME OUTCOMES

1. Understand the world, their country, their society, as well as themselves and have awareness of ethical problems, social rights, values and responsibility to the self and to others. 1

2. Understand different disciplines from natural and social sciences to mathematics and art, and develop interdisciplinary approaches in thinking and practice. 3

3. Think critically, follow innovations and developments in science and technology, demonstrate personal and organizational entrepreneurship and engage in life-long learning in various subjects; have the ability to continue to educate him/herself. 3

4. Communicate effectively in Turkish and English by oral, written, graphical and technological means. 3

5. Take individual and team responsibility, function effectively and respectively as an individual and a member or a leader of a team; and have the skills to work effectively in multi-disciplinary teams. 2

1. Possess sufficient knowledge of mathematics, science and program-specific engineering topics; use theoretical and applied knowledge of these areas in complex engineering problems. 5

2. Identify, define, formulate and solve complex engineering problems; choose and apply suitable analysis and modeling methods for this purpose. 3

3. Develop, choose and use modern techniques and tools that are needed for analysis and solution of complex problems faced in engineering applications; possess knowledge of standards used in engineering applications; use information technologies effectively. 1

4. Have the ability to design a complex system, process, instrument or a product under realistic constraints and conditions, with the goal of fulfilling specified needs; apply modern design techniques for this purpose. 1

5. Design and conduct experiments, collect data, analyze and interpret the results to investigate complex engineering problems or program-specific research areas. 1

6. Possess knowledge of business practices such as project management, risk management and change management; awareness on innovation; knowledge of sustainable development. 1

7. Possess knowledge of impact of engineering solutions in a global, economic, environmental, health and societal context; knowledge of contemporary issues; awareness on legal outcomes of engineering solutions; knowledge of behavior according to ethical principles, understanding of professional and ethical responsibility. 1

8. Have the ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. 1

1. Develop knowledge of theories, concepts, and research methods in humanities and social sciences. 1

2. Assess how global, national and regional developments affect society. 1

3. Know how to access and evaluate data from various sources of information. 1

### ASSESSMENT METHODS and CRITERIA

 Percentage (%) Final 30 Midterm 44 Quiz 16 Assignment 5 Participation 10