470-8722/01 – Mathematical Analysis II (MA2NT)
| Gurantor department | Department of Applied Mathematics | Credits | 6 |
| Subject guarantor | Mgr. Bohumil Krajc, Ph.D. | Subject version guarantor | Mgr. Bohumil Krajc, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 2 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2010/2011 | Year of cancellation | |
| Intended for the faculties | USP, FEI, HGF, FMT | Intended for study types | Bachelor |
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
Additional study materials
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
Other requirements
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction