470-2110/03 – Mathematical Analysis 1 (MA1)
| Gurantor department | Department of Applied Mathematics | Credits | 5 |
| 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 | winter |
| | Study language | Czech |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FEI | 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 one-variable real functions.
Teaching methods
Lectures
Tutorials
Project work
Summary
In the first part of this subject, there are fundamental properties of the set of real numbers mentioned. Further, basic properties of elementary functions are recalled. Then limit of sequence, limit of function, and continuity of function are defined and their basic properties are studied. Differential and integral calculus of one-variable real functions is essence of this course.
Compulsory literature:
J. Bouchala, M. Sadowská: Mathematical Analysis I (www.am.vsb.cz/bouchala)
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
Tests, individual work.
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:
Real Number System.
Real Functions of a Single Real Variable.
Elementary Functions.
Sequences of Real Numbers.
Limit and Continuity of a Function.
Differential and Derivative of a Function.
Basic Theorems of Differential Calculus.
Function Behaviour.
Approximation of a Function by a Polynomial.
Antiderivative (Indefinite Integral).
Riemann’s (Definite) Integral.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction