470-4123/01 – Elements of Higher Mathematics (EVM)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantorMgr. Bohumil Krajc, Ph.D.Subject version guarantorMgr. Bohumil Krajc, Ph.D.
Study levelundergraduate or graduateRequirementOptional
Year1Semesterwinter
Study languageCzech
Year of introduction2016/2017Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRA04 Mgr. Bohumil Krajc, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 10+10

Subject aims expressed by acquired skills and competences

A successful student of the course will have the knowledge and skills of a typical graduate bachelor degree in Computational Mathematics .

Teaching methods

Lectures
Tutorials
Project work

Summary

Subject contains parts of higher mathematics omitted in some bachelor programs. Mastering selected parts is essential for the successful engineering degree in Computational Mathematics. In the field of differential calculus of of functions of several variables we concetrate on the following parts: differentiating of composite functions, Taylor polynomials, implicit function theorem, constrained extremes. Students also learn the basic principles and methods of multidimensional integration. Attention to numerical methods is focused on issues of numerical differentiation and integration of functions. Some remarks are dedicated to a function approximation, search for zero points and extremal tasks. A substantial part of the course is the interpretation of the relevant passages in the field of ordinary differential equations and their systems.

Compulsory literature:

• W. Rudin, Principles of Mathematical Analysis, McGraw-Hill Book Company, New York, 1964 • W. E. Boyce, R. C. DiPrima: Elementary differential equations. Wiley, New York 1992

Recommended literature:

• M. Braun: Differential Equations and Their Applications. Springer, Berlin 1978.

Way of continuous check of knowledge in the course of semester

Students pass out tests and deliver projects.

E-learning

Další požadavky na studenta

No additional requirements are imposed on students.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1.Diferential of a function of several variables. Gradient method. 2.Diferential of a composite function. Transformation of variables in the differential expressions. 3.Approximation of function . Taylor's theorem . Conditions for the existence of local extremes. 4.Numerical derivative. Approximate solutions of equations. 5.Theorem about implicitly defined function. Constrained extremes. 6.Construction of integral sums, numerical integration . 7.Definition of multiple integrals. Selected applications. 8.Fubini`s theorems. Substitution in multiple integrals . Geometric interpretation of Jacobian . 9.Theorems about the existence and uniqueness of solutions of initial value problems for ordinary differential equations. Euler's method. 10.Transformation of variables in differential equations . 11.Potential and its use for solving exact equations. 12.Ordinary differential equations of higher orders. Solving linear differential equations. Boundary value problems .

Conditions for subject completion

Full-time form (validity from: 2016/2017 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  10
        Examination Examination 70  21
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 1 Optional study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC P Czech Ostrava 1 Optional study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava 1 Optional study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC K Czech Ostrava 1 Optional study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner