470-2106/01 – Mathematical Analysis II (MA2PM)

Gurantor departmentDepartment of Applied MathematicsCredits8
Subject guarantorMgr. Bohumil Krajc, Ph.D.Subject version guarantorMgr. Bohumil Krajc, Ph.D.
Study levelundergraduate or graduateRequirementChoice-compulsory
Year2Semesterwinter
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFEIIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRA04 Mgr. Bohumil Krajc, Ph.D.
VLA04 Ing. Oldřich Vlach, 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:

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

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

Continuous assessment: Students will keep homework and projects. During the semester will be held two written tests rated in total a maximum of 20 points. The projects can acquire a maximum 10 points. Terms of the credit: Credit will be granted if the student receives written tests and projects at least 10 points.

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:

Lectures: 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 on the links between the basic 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 for the existence of local extreme. Constrained local extrema, Lagrange multipliers method. Search global extremes - practices. Riemann double integral, basic properties. Fubini's theorem for double integrals. Substitution theorem for double integrals, applications, Riemann double integral triple integrals, basic properties. Fubini theorem for integrals. Substitution theorem for integrals. Applications. Practice: Investigation of different topological and metric properties of subsets eukleidovského space. Determining the limit of a sequence of points in Euclidean space. Discussion of terms limits and continuity of functions of several variables. Methods of calculating the limit, the verification link. The calculations of partial derivatives and directional derivatives. Gradient. Geometric interpretation. Calculations of higher order differentials. Application of Taylor's theorem for functions of several variables. Working with functions defined implicitly. Search for extremes of functions of several variables - local and constrained local extremes. Finding the global minima. Calculation of double integrals - Fubini's theorem. Calculation of double inegrálu - substitution to polar coordinates. Applications. The calculation of triple integrals - Fubini's theorem. Substitution into cylindrical and spherical coordinates. Applications of triple integrals. Projects: Solving difficult problems of differential and integral calculus of functions of several 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
2014/2015 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 2 Choice-compulsory study plan
2014/2015 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 2 Choice-compulsory study plan
2013/2014 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 2 Choice-compulsory study plan
2013/2014 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 2 Choice-compulsory study plan
2012/2013 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 2 Choice-compulsory study plan
2012/2013 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 2 Choice-compulsory study plan
2011/2012 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 2 Choice-compulsory study plan
2011/2012 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 2 Choice-compulsory study plan
2010/2011 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 2 Choice-compulsory study plan
2010/2011 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 2 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner