470-8722/01 – Mathematical Analysis II (MA2NT)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantorMgr. Bohumil Krajc, Ph.D.Subject version guarantorMgr. Bohumil Krajc, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year2Semesterwinter
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFEI, HGF, FMT, USPIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRA0220 Ing. Jan Kracík, Ph.D.
KRA04 Mgr. Bohumil Krajc, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+3
Combined Credit and Examination 3+3

Subject aims expressed by acquired skills and competences

Succesful student will gain deep and wide knowledge of the subject.

Teaching methods

Lectures
Tutorials

Summary

The subject consists of the basic parts of the n-dimensional calculus theory and practice.

Compulsory literature:

Tom M. Apostol: Calculus, Volume 2, Multi-variable calculus and linear algebra with applications to differential equations and probability, Wiley, New York, 1969 W. E. Boyce, R. C. DiPrima: Elementary differential equations. Wiley, New York 1992

Recommended literature:

W. Rudin: Principles of Mathematical Analysis. McGraw-Hill Book Company, New York 1964

Way of continuous check of knowledge in the course of semester

Students will be continuously addressed assigned projects. During the semester will be held written tests. Terms of the credit: Credit will be awarded to students who successfully manage tests and in those terms, work on projects.

E-learning

Další požadavky na studenta

There are not defined other requirements for student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Real functions of several variables. Euclidean spaces. Topological properties of subsets of Euclidean metric space. Limits and continuity. Partial derivative, the concept of directional derivatives. Total differential and the gradient function. Applications. Geometric interpretation gradient, outline methods steepest descent method. Discussion relationships between the fundamental concepts of calculus. Differentials of higher orders, Taylor polynomials, Taylor's theorem. Theorem of implicit function. Weierstrass theorem on the global extrema, local extrema. Criteria existence of local extreme. Constrained local extrema, Lagrange multipliers method. Search global extremes - practices. Riemann double integral, basic properties. Fubini phrases in double integrals. Substitution theorem for double integrals, applications of double integrals Riemann triple integrals, basic properties. Fubini theorems for integrals. Substitution theorem for integrals. Applications. First order differential equations, the theorem on the existence and uniqueness of the Cauchy problem. Linear differential equation 1 order, the equation with separated variables.

Conditions for subject completion

Full-time form (validity from: 2012/2013 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation 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 (B3942) Nanotechnology (3942R001) Nanotechnology P Czech Ostrava 2 Compulsory study plan
2019/2020 (B3942) Nanotechnology (3942R001) Nanotechnology P English Ostrava 2 Compulsory study plan
2019/2020 (B0719A270001) Nanotechnology P Czech Ostrava 1 Compulsory study plan
2019/2020 (B1701) Physics (1702R001) Applied Physics P Czech Ostrava 2 Compulsory study plan
2018/2019 (B3942) Nanotechnology (3942R001) Nanotechnology P Czech Ostrava 2 Compulsory study plan
2018/2019 (B3942) Nanotechnology (3942R001) Nanotechnology P English Ostrava 2 Compulsory study plan
2018/2019 (B1701) Physics (1702R001) Applied Physics P Czech Ostrava 2 Compulsory study plan
2017/2018 (B1701) Physics (1702R001) Applied Physics P Czech Ostrava 2 Compulsory study plan
2017/2018 (B3942) Nanotechnology (3942R001) Nanotechnology P Czech Ostrava 2 Compulsory study plan
2016/2017 (B3942) Nanotechnology (3942R001) Nanotechnology P Czech Ostrava 2 Compulsory study plan
2016/2017 (B1701) Physics (1702R001) Applied physics P Czech Ostrava 2 Compulsory study plan
2016/2017 (B1701) Physics (1702R001) Applied Physics P Czech Ostrava 2 Compulsory study plan
2015/2016 (B1701) Physics (1702R001) Applied physics P Czech Ostrava 2 Compulsory study plan
2015/2016 (B3942) Nanotechnology P Czech Ostrava 2 Compulsory study plan
2015/2016 (B3942) Nanotechnology (3942R001) Nanotechnology P Czech Ostrava 2 Compulsory study plan
2014/2015 (B1701) Physics (1702R001) Applied physics P Czech Ostrava 2 Compulsory study plan
2014/2015 (B3942) Nanotechnology P Czech Ostrava 2 Compulsory study plan
2013/2014 (B1701) Physics (1702R001) Applied physics P Czech Ostrava 2 Compulsory study plan
2013/2014 (B3942) Nanotechnology P Czech Ostrava 1 Compulsory study plan
2013/2014 (B3942) Nanotechnology P Czech Ostrava 2 Compulsory study plan
2012/2013 (B3942) Nanotechnology P Czech Ostrava 2 Compulsory study plan
2012/2013 (B3942) Nanotechnology (3942R001) Nanotechnology P Czech Ostrava 2 Compulsory study plan
2011/2012 (B3942) Nanotechnology P Czech Ostrava 2 Compulsory study plan
2010/2011 (B3942) Nanotechnology P Czech Ostrava 2 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner