470-8746/01 – Differential and Integral Calculus of Functions of Real and Complex Variables (DIP)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantorprof. RNDr. Jiří Bouchala, Ph.D.Subject version guarantorprof. RNDr. Jiří Bouchala, Ph.D.
Study levelundergraduate or graduate
Study languageCzech
Year of introduction2016/2017Year of cancellation
Intended for the facultiesUSPIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
BER95 doc. Ing. Petr Beremlijski, Ph.D.
BOU10 prof. RNDr. Jiří Bouchala, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+3

Subject aims expressed by acquired skills and competences

Upon the successful completion of the course, students will be able to actively use new terms in the field of differential and integral calculus.

Teaching methods

Lectures
Tutorials

Summary

The aim of the course Differential and Integral Calculus of Functions of Real and Complex Variables is to introduce students to differential and integral calculus of real and complex functions including functional series. Simultaneously, they should acquire a certain computational skill and ability to apply the taught theory on practical problems.

Compulsory literature:

1. James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics, Addison-Wesley Publishing Company, 1994.

Recommended literature:

1. James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994. 2. William L. Briggs, Van Emden Henson: An Owner’s Manual for the Discrete Fourier Transform, SIAM, 1995, ISBN 0-89871-342-0. 3. Michael W. Frazier: An introduction to wavelets through Linear Algebra, Springer, 1999, ISBN 0-387-98639-1

Way of continuous check of knowledge in the course of semester

During the semester we will write two tests.

E-learning

Další požadavky na studenta

There are no additional requirements on a student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures + exercises: Multi-variable Differential and Integral Calculus of Real Functions. 1.Sequence Convergence. Limits, Functions, and Continuity. 2.Total Differential, Partial Derivatives, Directional Derivative, Gradient. 3.Higher Order Differentials, Taylors Polynomial, Taylor’s Theorem. 4.Implicit Function Theorem. 5.Local, Global, and Constrained Extrema, Lagrange multipliers. 6.Double and Triple Integral. Fubini’s Theorem for Double and Triple Integral. 7.Substitution Theorem. Application of Multiple Integrals. Functions of a Complex Variable. 8.Complex Numbers, Extended Gaussian Images. 9.Complex Functions of a Real and Complex variable. 10.Limits, Continuity, and Complex Functions Derivatives. Conformal Mapping. 11.Complex Function Integration, Cauchy Theorem. 12.Power and Taylor Series. Laurent Series. Rezidue Theorem. 13.Scalar Multiplication, Norm, Orthogonal Systems. 14.Fourier Series.

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
2018/2019 (N2658) Computational Sciences (2612T078) Computational Sciences P Czech Ostrava 1 Compulsory study plan
2017/2018 (N2658) Computational Sciences (2612T078) Computational Sciences P Czech Ostrava 1 Compulsory study plan
2016/2017 (N2658) Computational Sciences (2612T078) Computational Sciences P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner