470-8723/02 – Mathematical Analysis II (MA2AVAT)
Gurantor department | Department of Applied Mathematics | Credits | 4 |
Subject guarantor | prof. RNDr. Jiří Bouchala, Ph.D. | Subject version guarantor | prof. RNDr. Jiří Bouchala, 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 | USP, FS | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
Students will get basic practical skills for work with fundamental concepts, methods and applications of differential and integral calculus of multivariable functions.
Teaching methods
Lectures
Tutorials
Summary
This subject contains 2 basic themes:
differential and integral calculus of multivariable real functions.
Compulsory literature:
J. Stewart: Calculus, 2008 Thomson
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
Tests, individual work.
E-learning
Other requirements
Additional requirements for students are not.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Differential calculus of multivariable functions
Real functions of several variables.
Limits and continuity.
Partial derivative, gradient and directional derivative, total differential.
Differentials of higher orders, Taylor polynomials, Taylor's theorem.
Implicit function theorem.
Local, constrained and global extrema. Lagrange multipliers method.
2. Integration of multivariable functions
Riemann double and triple integrals.
Fubini theorem.
Substitution theorem for double and triple integrals.
Applications of double and triple integrals.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.