Calculus I

Course Code:

MATH 131

Course Period:

Autumn

Course Type:

Core

Credits:

4

Theoric:

3

Practice:

2

ECTS:

6

Course Language:

English

Course Objectives:

The aim of this course is to provide students with an understanding of limits, derivatives and integrals of functions of one variable and their calculations.

Course Content:

Limits and continuity. Derivatives. Rules of differentiation. Applications of derivatives; extreme values, sketching graphs of functions. Definite Integrals, the fundamental theorems of calculus. Methods of integration. Applications of integrals; areas of plane regions, volumes of solids of revolution, arc length, areas of surfaces of revolution.

Course Methodology:

1: Lecture, 2: Problem Solving

Course Evaluation Methods:

A: Written examination

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Course Learning Outcomes

Learning Outcomes	Program Outcomes	Teaching Methods	Assessment Methods
1) Knows the concepts of limits and continuity of functions of a single variable and performs related calculations.	1	1,2	A
2) Knows the concept of derivative and some of its applications and performs related calculations.	1	1,2	A
3) Knows the concepts of definite, indefinite and improper integrals and some of their applications and performs related calculations.	1	1,2	A

Course Flow

Week	Topics	Study Materials
1	Limits of functions, Limits at infinity and infinite limits	(From textbook) 1.2,1.3
2	Continuity, The formal definition of limit, Tangent lines and their slopes, The derivative	1.4,1.5,2.1,2.2
3	Differentiation rules, The chain rule, Derivatives of trigonometric functions	2.3,2.4,2.5
4	Higher order derivatives, The Mean-Value Theorem, Implicit differentiation, Antiderivatives and Initial-Value Problems	2.6,2.8,2.9,2.10
5	Inverse functions, Exponential and logarithmic functions, The natural logarithm and exponential	3.1,3.2,3.3
6	The inverse trigonametric functions, Related rates	3.5,4.1
7	Indeterminate forms, Extreme values, Concavity and inflections	4.3,4.4,4.5
8	Sketching the graph of a function, Extreme-value problems, Linear approximations	4.6,4.8,4.9
9	Sums and sigma notation, Areas as limits of sums, The definite integral, Properties of the definite integral, The Fundamental Theorem of Calculus	5.1,5.2,5.3,5.4,5.5
10	The method of substitution, Areas of plane regions	5.6,5.7
11	Integration by parts, Integrals of rational functions	6.1,6.2
12	Inverse substitutions, Improper integrals	6.3,6.5
13	Volumes by slicing - Solids of revolution	7.1,7.2
14	Arc Length and surface area	7.3

Recommended Sources

Textbook	R. A. Adams and C. Essex, Calculus, 7th Ed., Pearson (2010)
Additional Resources

Material Sharing

Documents
Assignments
Exams

Assessment

IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	2	100
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE	1	40
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		60
Total		100

Course’s Contribution to Program

COURSE'S CONTRIBUTION TO PROGRAM
No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied information in these areas to model and solve engineering problems.					X
2	Ability to identify, formulate, and solve Electrical and Electronics Engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.
3	Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose.
4	Ability to devise, select, and use modern techniques and tools needed for engineering practice; ability to employ information technologies effectively.
5	Ability to design and conduct experiments, gather data, analyze and interpret results for investigating engineering problems
6	Ability to access information; For this purpose ability to perform database searching and conduct literature review.
7	Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
8	Ability to communicate effectively both orally and in writing; knowledge of a minimum of one foreign language.
9	Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
10	Awareness of professional and ethical responsibility.
11	Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.
12	Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of engineering solutions.

ECTS

ctivities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (14x Total course hours)	14	6	84
Hours for off-the-classroom study (Pre-study, practice)	14	3	42
Mid-terms (Including self study)	2	8	16
Final examination (Including self study)	1	12	12
Total Work Load			154
Total Work Load / 25 (h)			6.16
ECTS Credit of the Course			6

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Calculus I

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