714-0513/03 – Special Topics in Mathematics (VKM)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 5 |
| Subject guarantor | prof. RNDr. Radek Kučera, Ph.D. | Subject version guarantor | prof. RNDr. Radek Kučera, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | English |
| Year of introduction | 2015/2016 | Year of cancellation | 2019/2020 |
| Intended for the faculties | HGF | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
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
analyze problems, distinguish between important and unimportant, suggest a
method of solution, verify each step of a method, generalize achieved results,
analyze 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.
Teaching methods
Lectures
Individual consultations
Tutorials
Other activities
Summary
Basics of vector calculus. Functions of several variables: partial differentiation,
extremal values. Integral calculus of functions of two variables and its application.
Line integral and its applications. Basics of vector fields.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Tests and credits
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Exercises
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Conditions for obtaining credit points (CP):
- participation in exercises, 20% can be to apologize
- completion of three written tests, 0-15 CP
- completion of two programs, 5 CP
Exam
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- written exam 0-60 CP, successful completion at least 25 CP
- oral exam 0-20 CP, successful completion at least 5 CP
The exam questions are analogous to the program of the lectures.
E-learning
Other requirements
There are no other requirements on students.
Prerequisities
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Week. Lecture
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1st Vector calculus, scalar, cross and triple product, vector functions.
2nd Differential calculus of functions of two or more real variables: domain, graph, limit and continuity.
3rd Partial derivatives, total differential, tangent plane and normal to a surface.
4th Implicit function and its derivatives.
5th Extremes of functions, calculation via derivatives.
6th Constrained extremes, Lagrange's method.
7th Global extremes. Taylor's theorem.
8th Two-dimensional integrals on a rectangle and on a general domain.
9th Calculations of two-dimensional integrals, applications in geometry and physics.
10th Three-dimensional integrals, calculation and application.
11th Line integral of the first and second kind, calculation methods.
12th Applications of curved integrals, Green's theorem, independence of the integration path.
13th Surface integrals and their calculation.
14th Introduction to the field theory: gradient, potential, divergence rotation, Gauss-Ostrogradsky's and Stoke's theorem.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.