Mathematics 3

Објавено: June 28, 2022
1. Course Title Mathematics 3
2. Code 4ФЕИТ08З009
3. Study program КХИЕ,КСИАР,ЕЕПМ,ЕАОИЕ,ЕЕС,ТКИИ
4. Organizer of the study program (unit, institute, department) Faculty of Electrical Engineering and Information Technologies
5. Degree (first, second, third cycle) First cycle
6. Academic year/semester II/3 7. Number of ECTS credits 6
8. Lecturer D-r Sonja Gegovska Zajkova, D-r Vesna Andova
9. Course Prerequisites
 Passed: Mathematics 1
10. Course Goals (acquired competencies): Upon completion of the course, the student is able to: solve first-order differential equations and higher-order differential equations with constant coefficients; to calculate partial derivatives, double and triple integrals; to interpret the geometric meaning of total differential and double integrals; to apply differentiation and integration of functions of two and three variables in modeling and solving geometric and physical problems, to calculate curvilinear and surface integrals of scalar and vector type, to apply vector fields, as well as to analyze and solve problems in electrical engineering by combining the basic concepts and principles of differential and integral computation of a real function of two and three real variables; to think and reason logically, as well as to express itself precisely and clearly when presenting solutions; to pursue advanced mathematics courses and engineering courses in the upper academic years.

11. Course Syllabus: Differential equations: definition, solutions, existence uniqueness theorem. First-order differential equations: with separable variables, homogeneous, linear, and Bernoulli differential equation. Higher linear homogeneous differential equations with constant coefficients. Systems DR. Modeling with differential equations.

Basic concepts for multi-variable functions. Cylindrical and spherical coordinate system. Partial derivatives of functions of multiple variables. Total differential. Partial derivatives of complex function. Performance statement by direction. Gradient. Tangent plane and surface normal. Extreme values.

Double integrals and applications. Triple integrals and application.

Vector fields. Line integrals, scalar line integrals, vector line integrals. Conservative vector fields. Surface integrals. Application.
12. Learning methods: Blended teaching method: lecturing, tutorials supported by presentations and visualization of concepts, active participation of students through tests and assignments, all supported by learning management system.
13. Total number of course hours 3 + 3 + 0 + 0
14. Distribution of course hours 180
15. Forms of teaching 15.1. Lectures-theoretical teaching 45
15.2. Exercises (laboratory, practice classes), seminars, teamwork 45
16. Other course activities 16.1. Projects, seminar papers 0
16.2. Individual tasks 0
16.3. Homework and self-learning 90
17. Grading 17.1. Exams 30
17.2. Seminar work/project (presentation: written and oral) 0
17.3. Activity and participation 0
17.4. Final exam 70
18. Grading criteria (points) up to 50 points 5 (five) (F)
from 51to 60 points 6 (six) (E)
from 61to 70 points 7 (seven) (D)
from 71to 80 points 8 (eight) (C)
from 81to 90 points 9 (nine) (B)
from 91to 100 points 10 (ten) (A)
19. Conditions for acquiring teacher’s signature and for taking final exam Regular attendance at classes and realized tests
20. Forms of assessment During the semester, two partial written exams are provided (in the 8th and 15th week of the semester, lasting a maximum of 90 minutes), and tests can be conducted during the classes. In the planned exam sessions, a written exam is taken (duration up to 135 minutes). For students who have passed the partial exams, ie the written exam, a final oral exam can be conducted (duration up to 60 minutes). The final grade includes the points from the partial exams, ie the written exam, as well as the points from the tests and the final oral exam.
21. Language Macedonian and English
22. Method of monitoring of teaching quality Self-evaluation and surveys
23. Literature
23.1. Required Literature
No. Author Title Publisher Year
1 Douglas J. Faires, Barbara T. Faires Calculus Random House, New York 1988
2 Sonja Gegovska-Zajkova, Katerina Hadzi-Velkova Saneva Multivariable Calculus and Differential Equations (in Macedonian) FEIT 2015
23.2. Additional Literature
No. Author Title Publisher Year
1 Denis Auroux Multivariable Calculus https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/index.htm 2010