COURSE INFORMATION Course Title: CALCULUS I

Code	Course Type	Regular Semester	Theory	Practice	Lab	Credits	ECTS
MTH 101	A	1	3	2	0	4	7

Academic staff member responsible for the design of the course syllabus (name, surname, academic title/scientific degree, email address and signature)	NA
Main Course Lecturer (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	Dr. Shkëlqim Hajrulla shhajrulla@epoka.edu.al
Second Course Lecturer(s) (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	M.Sc. Eriselda Goga egoga@epoka.edu.al
Teaching Assistant(s) and Office Hours:	NA
Language:	English
Compulsory/Elective:	Compulsory
Study program: (the study for which this course is offered)	Bachelor in Electronics and Digital Communication Engineering (3 years)
Classroom and Meeting Time:	N/A
Code of Ethics:	Code of Ethics of EPOKA University Regulation of EPOKA University "On Student Discipline"
Attendance Requirement:	N/A
Course Description:	Functions, Limits, continuity and derivatives. Applications. Extreme values, the Mean Value Theorem and its applications. Graphing. The definite integral. Area and volume as integrals. The indefinite integral. Transcendental functions and their derivatives. L'Hopital's rule. Techniques of integration. Improper integrals. Applications. Parametric curves. Polar coordinates.
Course Objectives:	The objective of this course is to provide a good background on single variable calculus, including limits, derivatives, applications of derivatives, and integration.

BASIC CONCEPTS OF THE COURSE

1	Domains can also be explicitly specified, if there are values for which the function could be defined
2	A function that is both one-to-one and onto is called a one-to-one correspondence or bijective.
3	Since we are considering values on both sides of the point, this type of limit is sometimes referred to as a two-sided limit.
4	We can figure out the equation for this line by taking the limit of our equation as xx approaches infinity. This line is called an asymptote
5	In the definition of derivative, this ratio is considered in the limit as Δx → 0. Let us turn to a more rigorous formulation.
6	Techniques of Differentiation explores various rules including the product, quotient, chain, and power, exponential and logarithmic rules
7	We say that f has a local maximum at a if, for all x sufficiently close to a, f(a) ≥ f(x). b) We say that f has a local minimum at a if, for all x sufficiently close to a, f(a) ≤ f(x).
8	L'Hospital's Rule tells us that if we have an indeterminate form 0/0 or ∞/∞ all we need to do is differentiate the numerator and differentiate the denominator and then take the limit.
9	We saw how to solve one kind of optimization problem in the section where we found the largest and smallest value that a function would take on an interval.
10	Indefinite integrals, Riemann sums, definite integrals, application problems.

COURSE OUTLINE

Week	Topics
1	Functions and models.Overview of the essential functions.The domain and range.Odd and even functions.
2	New functions from old ones. One-to-one and onto functions. Bijections. Inverse functions.
3	The concept of the limit, precise definition. One-sided limits. Infinite limits, vertical asymptotes.
4	Limits at infinity, horizontal asymptotes. Indeterminate forms. The sandwich theorem. Continuity.
5	The concept of the derivative.The formal definition of the derivative.Constructing the table of der.
6	Techniques of differentiation. The sum, product, ratio and chain rule. Higher order derivatives.
7	Application of derivatives: Monotony and local extreme values. Concavity and inflection points. Sketching graphs of functions.
8	Midterm exam.
9	Applications of derivatives: mean value theorem, L'Hospital's rule.
10	Applications of derivatives: optimization problems.
11	Related rate problems. Implicit differentiation.
12	Introduction to integrals.The fundamental theorem of calculus.
13	Techniques of integration. The substitution rule, integration by parts, integration of rational functions.
14	Improper integrals.

Prerequisite(s):	-
Textbook(s):	Textbook: "STEWART CALCULUS Early Transcendentals", James Stewart (8th edition)
Additional Literature:	"Thomas' Calculus: Early Transcendentals", George B. Thomas Jr. (12th edition)
Laboratory Work:	-
Computer Usage:	-
Others:	No

COURSE LEARNING OUTCOMES

1	Students will be able to find limits of functions and determine continuity of functions.
2	Find derivatives of algebraic and some trigonometric functions, and use derivatives to solve applied problems.
3	Find integrals of some algebraic and trigonometric functions, and use integrals to solve applied problems.
4	Find indefinite and improper integrals using different integration techniques, apply L'Hopital's rule
5	Represent area as a definite integral and interpret the result in applications.

COURSE CONTRIBUTION TO... PROGRAM COMPETENCIES (Blank : no contribution, 1: least contribution ... 5: highest contribution)

No	Program Competencies	Cont.
Bachelor in Electronics and Digital Communication Engineering (3 years) Program
1	Engineering graduates with sufficient theoretical and practical background for a successful profession and with application skills of fundamental scientific knowledge in the engineering practice	5
2	Engineering graduates with skills and professional background in describing, formulating, modeling and analyzing the engineering problem, with a consideration for appropriate analytical solutions in all necessary situations.	5
3	Engineering graduates with the necessary technical, academic and practical knowledge and application confidence in the design and assessment of machines or mechanical systems or industrial processes with considerations of productivity, feasibility and environmental and social aspects.	5
4	Engineering graduates with the practice of selecting and using appropriate technical and engineering tools in engineering problems, and ability of effective usage of information science technologies.	4
5	Ability of designing and conducting experiments, conduction data acquisition and analysis and making conclusions.	4
6	Ability of identifying the potential resources for information or knowledge regarding a given engineering issue.	4
7	The abilities and performance to participate multi-disciplinary groups together with the effective oral and official communication skills and personal confidence.	4
8	Ability for effective oral and official communication skills in foreign language.	3
9	Engineering graduates with motivation to life-long learning and having known significance of continuous education beyond undergraduate studies for science and technology.	5
10	Engineering graduates with well-structured responsibilities in profession and ethics.	3
11	Engineering graduates who are aware of the importance of safety and healthiness in the project management, workshop environment as well as related legal issues.	2
12	Consciousness for the results and effects of engineering solutions on the society and universe, awareness for the developmental considerations with contemporary problems of humanity.	2

COURSE EVALUATION METHOD

Method	Quantity	Percentage
Homework	2	5
Midterm Exam(s)	1	35
Quiz	2	5
Final Exam	1	45
	Total Percent:	100%

ECTS (ALLOCATED BASED ON STUDENT WORKLOAD)

Activities	Quantity	Duration(Hours)	Total Workload(Hours)
Course Duration (Including the exam week: 16x Total course hours)	16	5	80
Hours for off-the-classroom study (Pre-study, practice)	16	2	32
Mid-terms	1	17	17
Assignments	1	6	6
Final examination	1	25	25
Other	3	5	15
Total Work Load:			175
Total Work Load/25(h):			7
ECTS Credit of the Course:			7

CONCLUDING REMARKS BY THE COURSE LECTURER

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