714-3625/01 – Applied Mathematics (AM)
Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 6 |
Subject guarantor | Mgr. Jiří Vrbický, Ph.D. | Subject version guarantor | Mgr. Jiří Vrbický, Ph.D. |
Study level | undergraduate or graduate | Requirement | Choice-compulsory |
Year | 1 | Semester | winter |
| | Study language | English |
Year of introduction | 2014/2015 | Year of cancellation | 2018/2019 |
Intended for the faculties | FMT | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
The goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods.
Students should learn how to:
analyze problems, suggest a method of solution, analyze correctness of achieved results with respect to given conditions, aply these methods while solving technical problems.
Teaching methods
Lectures
Individual consultations
Tutorials
Other activities
Summary
The course includes the function of a complex variable, the ground of the
operational or tensor calculus and equation of mathematical physics. The emphasis will be on the lectured methods application to the model tasks.
Compulsory literature:
[1] James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456
Recommended literature:
Way of continuous check of knowledge in the course of semester
Course-credit
-participation on tutorials is obligatory, 20% of absence can be apologized,
-elaborate programs,
-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.
Point quantification in the interval 100 - 91 90 - 81 80 - 71 70 - 61 60 - 51 50 - 0
ECTS grade A B C D E F
Point quantification in the interval 100 - 86 85 - 66 65 - 51 51 - 0
National grading scheme excellent very good satisfactory failed
E-learning
http://www.studopory.vsb.cz
http://mdg.vsb.cz/M/
http://am.vsb.cz/bouchala
http://am.vsb.cz/kozubek
Other requirements
No special requirements.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Complex numbers. Infinite complex number series.
2. Complex functions of a complex variable and mappings. Elementary functions of complex variable.
3. Complex differentiation. Cauchy - Riemann equations.
4. Integration of complex variable function. Cauchy´s theorems. Taylor´s and Laurent´s series.
5. Singularities,residues, applications. Tensor algebra. Scalar, vector, tensor. Operations.
6. Vector’s differential operations, properties. Tensor’s operations, properties.
7. Tensor’s differential operations. Base line, invariants.
8. Field theory. Scalar and vector field. Gradient, divergence, rotation. Gauss theorem.
9. Equations of mathematical physics. 2nd order partial linear differential equations.
10. Fourier’s method of solution.
11. Solution of the heat-conduction: one dimensional heat conduction equation.
12. Combination of variable method. Green’s function method.
13. Finite diference method. Explicit method. Implicite method. Crank-Nicolson method. Process stability, process konvergence.
14. Reserve.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction