310-2303/01 – Mathematics 3 (Math 3)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 5 |
| Subject guarantor | Mgr. Jiří Krček, Ph.D. | Subject version guarantor | Mgr. Jiří Krček, Ph.D. |
| Study level | undergraduate or graduate | | |
| | Study language | English |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FS, FEI, HGF, FAST, FMT, FBI | Intended for study types | Bachelor, Follow-up Master |
Subject aims expressed by acquired skills and competences
The aim of the subject is to extend the mathematical topics from the bachelor study. Students will become familiar with systems of linear differential equations, double, triple and line integrals and with basic concepts from field theory.
Teaching methods
Lectures
Seminars
Individual consultations
Other activities
Summary
Mathematics 3 is connected with Mathematics 1,2.
We have to stress that student can enrol in this course only if he passed the course Mathematics 1 and 2 or an equivalent course.
- Integral calculus of functions of more than one variable
- Double and volume integral. Fubini's Theorem: integrating over regular regions.
- Transformation of variables, polar, cylindrical and spherical coordinates.
- Practical applications of double and volume integral.
- Theory of the field. Scalar and vector fields.
- Curves and their orientation, line integral of a scalar function and its geometrical applications.
- Line integral of a vector function and its physical applications.
- Path independence, Green's theorem.
Compulsory literature:
Lectures in English on school Moodle system - lms.vsb.cz
Recommended literature:
Neustupa J., Kračmar S.: Mathematics II. ČVUT, Praha 1998.
http://www.studopory.vsb.cz/studijnimaterialy/MatematikaIII/Matematika3_obsah.pdf (in czech language)
Additional study materials
Way of continuous check of knowledge in the course of semester
Course-credit
-participation on tutorials is obligatory, 20% of absence can be apologized,
-pass the written tests.
Point classification: 5-20 points.
Exam
Practical part of an exam is classified by 0 - 60 points. Practical part is successful if student obtains at least 25 points.
Theoretical part of the exam is classified by 0 - 20 points. Theoretical part is successful if student obtains at least 5 points.
Final classification:
100 - 91 90 - 81 80 - 71 70 - 61 60 - 51 50 - 0
A B C D E F
E-learning
http://www.studopory.vsb.cz/studijnimaterialy/MatematikaIII/Matematika3_obsah.pdf (in czech language)
http://mdg.vsb.cz
Other requirements
No more requirements are put on the student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Double integral and its applications.
2. Triple integral and its applications.
3. Theory of the field, scalr and vector fields.
4. Line integrals a nd their applications.
5. Systems of ODE, elimination and Euler's method.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.