# 470-2111/04 – Mathematical Analysis 2 (MA2)

 Gurantor department Department of Applied Mathematics Credits 3 Subject guarantor doc. Mgr. Petr Vodstrčil, Ph.D. Subject version guarantor doc. Mgr. Petr Vodstrčil, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester summer Study language English Year of introduction 2019/2020 Year of cancellation Intended for the faculties FEI Intended for study types Bachelor
Instruction secured by
VOD03 doc. Mgr. Petr Vodstrčil, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent

### Subject aims expressed by acquired skills and competences

Students will learn about differential calculus of more-variable real functions. In the second part students will get the basic practical skills for working with fundamental concepts, methods and applications of integral calculus of more-variable real functions.

Lectures
Tutorials

### Summary

This subject contains following topics: ----------------------------------- differential calculus of two and more-variable real functions, integral calculus of more-variable real functions or differential equations (according to the version)

### Compulsory literature:

L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973.

### Recommended literature:

J. Bouchala, M. Sadowská: Mathematical Analysis I, VŠB-TUO.

### Way of continuous check of knowledge in the course of semester

Credit tests will be written during the semester.

### Other requirements

There are not defined other requirements for student.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Lectures: - More-variable real functions. Partial and directional derivatives, differential and gradient. - Taylor's theorem. - Extremes of more-variable real functions. - Definition of double integral, basic properties. Fubini theorems for double integral. - Transformation of double integral, aplications of double integral. - Definition of triple integral, basic properties. Fubini theorems for triple integral. - Transformation of triple integral, aplications of triple integral. Exercises: - More-variable real functions. Partial and directional derivatives, differential and gradient. - Taylor's theorem. - Extremes of more-variable real functions. - Definition of double integral, basic properties. Fubini theorems for double integral. - Transformation of double integral, aplications of double integral. - Definition of triple integral, basic properties. Fubini theorems for triple integral. - Transformation of triple integral, aplications of triple integral.

### Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Min. number of points