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:	M.Sc. Eriselda Goga egoga@epoka.edu.al , Tuesday 10 : 00 - 12:00
Second Course Lecturer(s) (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	NA
Teaching Assistant(s) and Office Hours:	NA
Language:	English
Compulsory/Elective:	Compulsory
Study program: (the study for which this course is offered)	Bachelor in Civil 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:	75%
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	Functions and models: A function is a binary relation between two sets that associates each element of the first set to exactly one element of the second set.
2	A Bijection function is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first se
3	Limits: A limit is the value that a function (or sequence) approaches as the input (or index) approaches some value.
4	In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
5	Techniques of differentiation: Differentiation is a process of finding a function that outputs the rate of change of one variable with respect to another variable.
6	Application of derivatives: Applications of differentiation include finding the slope, locating absolute or local extrema on a graph, linear approximation or estimating the velocity
7	Implicit differentiation: In mathematics, an implicit equation is a relation of the form R(x1, …, xn) = 0, where R is a function of several variables (often a polynomial).
8	Implicit differentiation: An implicit function is a function that is defined by an implicit equation, that relates one of the variables, considered as the value of the function, with the others considered as the arguments.
9	Integrals: An integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data.
10	Integrals: Integrals may be generalized depending on the type of the function as well as the domain over which the integration is performed.

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 derivatives
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	Applications of derivatives: mean value theorem, L'Hospital's rule.
9	Midterm exam.
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):	"STEWART CALCULUS Early Transcendentals", James Stewart (9th edition)
Additional Literature:	"Thomas' Calculus: Early Transcendentals", George B. Thomas Jr. (13th 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 Civil Engineering (3 years) Program
1	an ability to apply knowledge of mathematics, science, and engineering	5
2	an ability to design a system, component, or process to meet desired needs	4
3	an ability to function on multidisciplinary teams	4
4	an ability to identify, formulate, and solve engineering problems	5
5	an understanding of professional and ethical responsibility	3
6	an ability to communicate effectively	3
7	the broad education necessary to understand the impact of engineering solutions in a global and societal context	3
8	a recognition of the need for, and an ability to engage in life long learning	4
9	a knowledge of contemporary issues	3
10	an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice	3
11	skills in project management and recognition of international standards and methodologies	4

COURSE EVALUATION METHOD

Method	Quantity	Percentage
Homework	2	5
Midterm Exam(s)	1	30
Quiz	2	7.5
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

To be completed at the end of the semester.