Skip to main content
Skip header

ECTS Course Overview



Mathematics 3

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code714-0868/01
Number of ECTS Credits Allocated5 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle, Second Cycle
Year of Study *
Semester when the Course Unit is deliveredWinter, Summer Semester
Mode of DeliveryFace-to-face
Language of InstructionEnglish
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
ZID76Mgr. Arnošt Žídek, Ph.D.
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.
- 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.
Learning Outcomes of the Course Unit
Goals and competence

Mathematics is essential part of education on technical universities.
It should be considered rather the method in the study of technical
courses than a goal. Thus the goal of mathematics is train logical
reasoning than mere list of mathematical notions, algorithms and
methods.
Students should learn how to
analyse problems,
distinguish between important and unimportant,
suggest a method of solution,
verify each step of a method,
generalize achieved results,
analyse correctness of achieved results with respect to given conditions,
apply these methods while solving technical problems,
understand that mathematical methods and theoretical advancements
outreach the field mathematics.
It is necessary to complete Mathematics 1 and Mathematics 2 courses or their
equivalents.
Course Contents
Course description (weekly lessons):

1. Double integral over rectangular region.
2. Double integral over regular region. Fubini's Theorem.
3. Transformation of variables. Mapping and its Jacobian. Polar coordinates.
4. Practical applications of double integral.
5. Volume integral over rectangular region.
6. Volume integral over regular region.
7. Transformation to the cylindrical coordinates.
8. Transformation to the spherical coordinates.
9. Practical applications of volume integral.
10. Curves in R^3. Their equations and orientation of closed curves.
11. Line integral of a scalar function.
12. Line integral of a vector function.
13. Path independence. Green's Theorem.
14. Practical applications of line integrals of both kinds.
Recommended or Required Reading
Required Reading:
http://mdg.vsb.cz/wiki/public/Double_Integral.pdf
http://mdg.vsb.cz/wiki/public/Double_Integral.pdf
Recommended Reading:
Neustupa J., Kračmar S.: Mathematics II. ČVUT, Praha 1998.
http://www.studopory.vsb.cz/studijnimaterialy/MatematikaIII/Matematika3_obsah.pdf (in czech language)
Neustupa J., Kračmar S.: Mathematics II. ČVUT, Praha 1998.
http://www.studopory.vsb.cz/studijnimaterialy/MatematikaIII/Matematika3_obsah.pdf (in czech language)
Planned learning activities and teaching methods
Lectures, Individual consultations, Other activities
Assesment methods and criteria
Tasks are not Defined