470-4121/02 – Selected Parts of Applied Mathematics (VKzAM)
Gurantor department | Department of Applied Mathematics | Credits | 4 |
Subject guarantor | doc. Mgr. Petr Vodstrčil, Ph.D. | Subject version guarantor | doc. Mgr. Petr Vodstrčil, Ph.D. |
Study level | undergraduate or graduate | Requirement | Optional |
Year | 2 | Semester | winter |
| | Study language | English |
Year of introduction | 2015/2016 | Year of cancellation | |
Intended for the faculties | FEI | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
After completing the course the student will be able to work with more-variable real functions. He will be able to find extremes of such functions. In addition, the student will be able to calculate the derivative of functionals and also seek their extremes.
Teaching methods
Lectures
Tutorials
Summary
This subject contains the following themes:
- more-variable functions, extremes
- function spaces
- functionals and their extremes
- applications
Compulsory literature:
H. Anton, I. Bivens, S. Davis: Calculus, 2009
L.E. Elsgolc: Calculus of Variations, 2007
Recommended literature:
L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973.
Way of continuous check of knowledge in the course of semester
During the semester we will write two tests.
E-learning
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 functions, partial derivatives, Schwarz theorem
- gradient
- relative extremes
- extremum problems with constraints
- absolute extremes
- numerical methods
- linear spaces, norm linear spaces
- function spaces, functionals
- derivative of functional
- extremes of functionals, Euler-Lagrange equation
- applications
Exercises:
- more-variable functions, partial derivatives, Schwarz theorem
- gradient
- relative extremes
- extremum problems with constraints
- absolute extremes
- numerical methods
- linear spaces, norm linear spaces
- function spaces, functionals
- derivative of functional
- extremes of functionals, Euler-Lagrange equation
- applications
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction