# 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
Instruction secured by
VRB50 Mgr. Jiří Vrbický, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+2
Part-time Credit and Examination 20+0

### 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

### 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

Full-time form (validity from: 2014/2015 Winter semester, validity until: 2018/2019 Summer semester)
Min. number of pointsMax. počet pokusů
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 20  5
Examination Examination 80 (80) 30 3
písemka Written test 60  25
teorie Oral examination 20  5
Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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### Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2018/2019 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials P English Ostrava 1 Choice-compulsory study plan
2017/2018 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies P English Ostrava 1 Choice-compulsory study plan
2017/2018 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials P English Ostrava 1 Choice-compulsory study plan
2016/2017 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies P English Ostrava 1 Compulsory study plan
2016/2017 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials P English Ostrava 1 Choice-compulsory study plan
2015/2016 (N3923) Materials Engineering (3911T033) Material Recycling P Czech Ostrava 1 Choice-compulsory study plan
2015/2016 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies P Czech Ostrava 1 Compulsory study plan
2015/2016 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies K Czech Ostrava 1 Compulsory study plan
2015/2016 (N3923) Materials Engineering (3911T036) Advanced Engineering Materials P English Ostrava 1 Choice-compulsory study plan
2014/2015 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies P Czech Ostrava 1 Compulsory study plan
2014/2015 (N3922) Economics and Management of Industrial Systems (3902T042) Automation and Computing in Industrial Technologies K Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner