### Mathematics 1

#### Course Description

Real numbers and functions of one real variable. Limits of sequences. Limit of a real function of real variable. Derivative of a function and applications. Integrals and applications. Matrices, determinants and solving linear systems.

#### General Competencies

Acceptance of elementary concepts and methods in linear algebra. Mastering the basic knowledge and techniques of the differential and integral calculus of functions of one variable and applications.

#### Learning Outcomes

1. describe and apply basic concepts of course
2. describe, connect and interpret basic notions, results and methods from course
3. demonstrate fundamental skills from course such as differentiation, integration, calculation of limits, solving systems and others
4. apply basic methods and skills into practice
5. analyze problems and making conclusions by using mathematical reasoning
6. demonstrate skills of mathematical modelling and problem solving
7. demonstrate an ability for mathematical expression

#### Forms of Teaching

Lectures

Lectures are held in two cycles, 6 hours per week

Exams

Midterm and final exam

Exercises

Excercises are held one hour per week

Consultations

each lecturer one hour per week

Continuous Assessment Exam
Quizzes 0 % 20 % 0 % 20 %
Mid Term Exam: Written 0 % 40 % 0 %
Final Exam: Written 0 % 40 %
Exam: Written 0 % 80 %
##### Comment:

The scores achieved on short tests will be transferred to the score of the exam only in the case when it is in the interest of the student.

#### Week by Week Schedule

1. Mathematical logic. Sets. Functions. The set of natural numbers, integers, and rational numbers. Mathematical induction. Real numbers. Complex numbers.
2. Real functions of one real variable. Review of elementary functions.
3. Sequences. Accumulation points. Limit of a sequence.
4. Limit of a real function of one real variable. Continuity of functions. Basic theorems about continuous functions.
5. Derivative of a function. Differentiation rules. Differentiation of implicit and parametric functions.
6. Differential of a function. Basic theorems of Differential Calculus. Lagrange mean value theorem. Taylor's theorem. L'Hospital's rule.
7. Finding extrema of a function. Convexity and concavity of a function. Sketching curves and qualitative graph of a function.
8. Midterm exam.
9. The indefinite and the definite integral. Methods of the integration (the substitution method and the integration by parts).
10. Integration of rational functions. Integration of some irrational and trigonometric functions.
11. The improper integral. Finding the area of planar sets. Computation of the length of curves. Finding the volume of the revolution. Finding surface of the revolution.
12. Matrices. Summation and the scalar multiplication. Multiplication of matrices. Properties of matrix multiplication. Determinants and their properties.
13. Inverse of a matrix. Rank of a matrix.
14. Solving linear systems of equations using the Gauss method. Finding eigenvalues and eigenvectors of quadratic matrices.
15. Final exam.

#### Study Programmes

Electrical Engineering and Information Technology and Computing (study)
(1. semester)

#### Literature

N. Elezović (1999.), Linearna algebra, Element
P. Javor (1999.), Matematička analiza 1, Element
M. Pašić (2004.), Matematička analiza 1, Merkur ABD
M. Pašić (2004.), Matematička analiza 2, Merkur ABD

#### General

ID 86475
Winter semester
7 ECTS
L0 English Level
L2 e-Learning
90 Lectures
15 Exercises
0 Laboratory exercises
0 Project laboratory