470-2112/02 – Repetition of Mathematical Analysis (RMA)
Gurantor department | Department of Applied Mathematics | Credits | 8 |
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 | 2 | Semester | winter |
| | Study language | English |
Year of introduction | 2015/2016 | Year of cancellation | 2020/2021 |
Intended for the faculties | FEI | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
The main objective of the course is to deepen knowledge and understanding of the basics of differential and integral calculus of real functions of one and more variables.
Teaching methods
Lectures
Tutorials
Project work
Summary
This subject contains 2 basic themes:
differential and integral calculus of one and multivariable real functions.
Compulsory literature:
J. Bouchala, M. Sadowská: Mathematical Analysis I, http://am.vsb.cz/bouchala
W. Rudin: Principles of Mathematical Analysis, McGraw-Hill, Inc.
Recommended literature:
H. Anton, I. Bivens, S. Davis: Calculus, John Wiley & sons, Inc.
Way of continuous check of knowledge in the course of semester
Studenti v průběhu semestru budou psát písemné testy a vypracují zadané projekty. Za testy lze získat maximálně 24 body, za projekty 6 bodů.
Podmínky udělení zápočtu:
K získání zápočtu je nutné získat minimálně 10 bodů.
E-learning
Other requirements
No additional requirements are imposed on the student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures:
1. Basic ideas of set theory.
2. Cardinality of sets.
3. Real numbers.
4. Sequences, limit of sequence.
5. Infinite series, criteria for convergence.
6. Exponential function, goniometric functions.
7. Sequence of functions, convergence.
8. Continuities of functions.
9. Differentiation of function . Implicit function theorem.
10. Extremes of function.
11. Weierstrass theorem .
12. Taylor´s polynomial.
13. Riemann integral.
14. Integration of functions of several real variables.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.