COURSE INFORMATION Course Title: MATH. FOR ECONOMICS AND BUSINESS II

Code	Course Type	Regular Semester	Theory	Practice	Lab	Credits	ECTS
BUS 102	A	2	2	2	0	3	5

Academic staff member responsible for the design of the course syllabus (name, surname, academic title/scientific degree, email address and signature)	Dr. Valmir Bame vbame@epoka.edu.al
Main Course Lecturer (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	M.Sc. Dafina Muda dshehi@epoka.edu.al , Friday 11:30- 14:30
Second Course Lecturer(s) (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	NA
Language:	English
Compulsory/Elective:	Compulsory
Study program: (the study for which this course is offered)	Bachelor in International Marketing and Logistics Management (3 years)
Classroom and Meeting Time:	Check the timetable.
Teaching Assistant(s) and Office Hours:	NA
Code of Ethics:	Code of Ethics of EPOKA University Regulation of EPOKA University "On Student Discipline"
Attendance Requirement:	Theory 60% , Practice 75%
Course Description:	Mathematics for Economics and Business II: Limits and Continuity. Average Rate of Change and Slope. Derivatives, Instantaneous Rate of Change, Higher Order Derivatives. Optimization, Concavity of Inflection Points. Maxima and Minima. Revenue, Cost and Profit Applications, Anti Derivatives, Rules of Integration, Differential Equations, Mathematics of Finance, Simple and Compound Interest, Present Value, Effective Interest, Future Value, Annuities.
Course Objectives:	The aim of this course is to give the basic ingredients of mathematics for business and economics. Namely, functions, derivatives and differentials. Moreover, most of the models in economics appear in the form of linear models.

BASIC CONCEPTS OF THE COURSE

1	Limits, slope, tangent
2	First-order derivative and second-order derivative of a function with one variable.
3	Marginal functions.
4	Stationary points, maximum, minimum.
5	Elasticity.
6	Partial derivative and second-order partial derivative of a function with two variables.
7	Maximum and minimum points of a function with two variables.
8	Integration. Definite integration.
9	Linear problems.
10	Differential equations.

COURSE OUTLINE

Week	Topics
1	Limits. Chapter 10 (Introductory Mathematical Analysis): an introduction to the basic idea of limit, rules of limits (Pages 451 - 469)
2	Differentiation. Chapter 4: an introduction to the basic idea of differentiation, derivative of power functions, exponential and natural logarithm functions, rules of differentiation. (Pages 275 - 297 and 312- 321)
3	Marginal Functions & Elasticity. Chapter 4 (continue): standard economic applications of differentiation economic applications in marginal functions and in elasticity, (Pages 298 - 311 and 322 - 336)
4	Optimisation. Chapter 4 (continue): standard economic applications of differentiation in optimisation (Pages 337 - 368)
5	Partial Differentiation. Chapter 5: functions of some variables, partial elasticity and marginal functions, first and second-order partial derivatives of functions of two variables, the application of partial derivatives in economics. (Pages 400 - 429)
6	Unconstrained Optimization. Chapter 5 (continue): application of first and second-order partial derivatives of functions of two variables in unconstrained optimisation. (Pages 443 - 456)
7	Constraint Optimization. Chapter 5 (continue): application of first and second-order partial derivatives of functions of two variables in constrained optimisation, Lagrange multipliers (Pages 457 - 481)ves of functions of two variables in constrained optimisation, Lagrange multipliers (Pages 457 - 481). Midterm exam. Materials for midterm exam, the students must study at the end of the chapter four and five, multiple choice questions and examination questions, on page 376-388 and 474-482
8	Review. Exercises.
9	Midterm exam.
10	Indefinite integration. Techniques of integration. Chapter 6: integration of functions of one variable, methods and techniques of integration. (Pages 493 - 508)
11	Definite integration. Chapter 6 (continue): area surface under the graph of a function, producer’s and consumer’s surpluses (Pages 509 - 523)
12	Graphical solution of linear programming problems. Chapter 8: basic mathematical techniques and special cases when problems have either no solution or infinitely many solutions, economic problem as a linear programming problem (Pages 599 - 629)
13	Differential equations. Chapter 9: the complementary function of a difference equation, the particular solution of a difference equation, the complementary function of a differential equation, the particular solution of a differential equation (Pages 643 - 672)
14	Review. Exercises.

Prerequisite(s):
Textbook(s):	Ian Jacques, Mathematics for Economics and Business, the ninth edition, Pearson 2018
Additional Literature:	Knud Sydsaeter, Peter Hammond. Essential Mathematics for Economic Analysis, the fifth edition. Pearson 2016 Vasil Lino Matematika per Ekonomine dhe Biznesin 2 Tirane 2022
Laboratory Work:
Computer Usage:
Others:	No

COURSE LEARNING OUTCOMES

1	Estimate the derivative of a function by measuring the slope of a tangent.
2	Derive the relationship between marginal and average revenue
3	Differentiate complicated functions using a combination of rules.
4	Determine the price elasticity for general linear demand functions.
5	Use the first and the second-order derivative to find maximum and minimum points of a function with one variable.
6	Perform implicit differentiation.
7	Use the first and the second-order derivative to find maximum and minimum points of a function with two variables.
8	Use the method of Lagrange multipliers to solve constrained optimisation problems.
9	Use methods of integration to calculate the consumer’s surplus, producer’s surplus, capital stock formation
10	Use matrix inverses to solve systems of linear equations arising in economics.

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

No	Program Competencies	Cont.
Bachelor in International Marketing and Logistics Management (3 years) Program

COURSE EVALUATION METHOD

Method	Quantity	Percentage
Midterm Exam(s)	1	35
Quiz	2	5
Final Exam	1	45
Attendance		10
	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	4	64
Hours for off-the-classroom study (Pre-study, practice)	16	2	32
Mid-terms	1	10	10
Assignments			0
Final examination	1	15	15
Other	4	1	4
Total Work Load:			125
Total Work Load/25(h):			5
ECTS Credit of the Course:			5

CONCLUDING REMARKS BY THE COURSE LECTURER

The mathematical tools and techniques covered in this syllabus are not just academic exercises but essential skills for analyzing and solving real-world economic and business problems. Students’ commitment to learning and applying these principles will serve them well in their future academic and professional endeavors.