COURSE INFORMATION Course Title: BASIC MATHEMATICS

Code	Course Type	Regular Semester	Theory	Practice	Lab	Credits	ECTS
MTH 125	A	1	3	0	0	3	4

Academic staff member responsible for the design of the course syllabus (name, surname, academic title/scientific degree, email address and signature)	NA
Lecturer (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	Shkëlqim Hajrulla
Second 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
Classroom and Meeting Time:	A131 Tuesday 08:45
Course Description:	Each topic is considered in a way that assumes in the student average knowledge of the program of the high school. The theory is introduced in every topic as an essential definition, formulas, theorems, laws, and procedures. The practice problems and exercises are introduced as a correct application of the mathematical truths. Real architectural problems are presented as mathematical problems, aiming to improve the students’ ability to solve and to optimize them.
Course Objectives:	The course aims to further improve the students’ knowledge on the covered topics in high school in mathematics. This course will improve the students’ ability to utilize the mathematical knowledge in problem understanding, synthesis, and solution.

COURSE OUTLINE

Week	Topics
1	General overview on functions and their properties.
2	New functions from old ones. One-to-one and onto functions. Bijections.
3	The concept of the limit, precise definition. One-sided limits.
4	Indeterminate forms. Limits at infinity. Linear asymptotes.
5	The squeeze theorem. Continuity.
6	Derivatives. Formal definition. Differentiation rules.
7	Applications of derivatives: tangent and normal lines, monotony.
8	Midterm exam.
9	Applications of derivatives: concavity, the L'Hospital's rule.
10	Applications of derivatives: optimization problems.
11	Applications of derivatives: related rate problems.
12	Introduction to integrals.The fundamental theorem of calculus.
13	Integration techniques: integration by substitution.
14	Integration techniques: integration by parts.

Prerequisite(s):
Textbook:	«Calculus», James Stewart, 8-th edition
Other References:
Laboratory Work:
Computer Usage:
Others:	No

COURSE LEARNING OUTCOMES

1	Compute limits of algebraic functions graphically, numerically, and algebraically.
2	Compute the derivative of basic algebraic, exponential, and logarithmic functions using derivative rules and implicit differentiation.
3	Interpret the derivative graphically and as a rate of change in applications.
4	Apply derivatives in optimization problems.
5	Compute indefinite and definite integrals of functions using anti-derivative rules and the Fundamental Theorem of Calculus.
6	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.
Integrated second cycle study program in Architecture (5 years) Program

COURSE EVALUATION METHOD

Method	Quantity	Percentage
Midterm Exam(s)	1	30
Final Exam	1	70
	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	3	48
Hours for off-the-classroom study (Pre-study, practice)	16	1	16
Mid-terms	1	16	16
Assignments	1	5	5
Final examination	1	25	25
Other	3	5	15
Total Work Load:			125
Total Work Load/25(h):			5
ECTS Credit of the Course:			4