470-2102/02 – Mathematical Analysis I (MA 1)
| 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 | Compulsory |
| Year | 1 | Semester | summer |
| | Study language | English |
| Year of introduction | 2015/2016 | Year of cancellation | 2020/2021 |
| Intended for the faculties | USP, 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
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, VŠB-TUO.
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 6 tests.
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:
Real numbers. Supremum and infimum. Principle of mathematical induction.
Real one-variable functions and their basic properties.
Elementary functions.
Sequences of real numbers. Limit of sequence.
Theorems on limit of sequences, calculation of limits.
Limit of a function. Theorems on limits.
Continuity of a function. Theorems on limits and continuity of composite function.
Derivative and differential of a function. Calculation of derivatives.
Basic theorems of differential calculus. L'Hospital rule.
Intervals of monotony of a function. Local extremes of a function.
Convexity and concavity. Asymptotes of graphs. Course of a function.
Global extremes of a function. Weierstrass-theorem.
Taylor's theorem.
Fundamental principles of integral calculus.
Exercises:
Application of principle of mathematical induction. Supremum and infimum of various sets.
Functions and their properties. Graph of a function. Functions with absolute value.
Elementary functions. Calculation of inverse function.
Finding domain of definition of a function. Arithmetic and geometric sequence.
Calculation of limits of sequences.
Calculation of limits of functions.
Limits of functions. Continuity of a function.
Calculation of derivatives.
Tangent and normal line. L'Hospital rule.
Monotony of a function. Local extremes.
Convexity and concavity, asymptotes. Course of a function.
Global extremes of a function.
Taylor's polynom and error estimation.
Calculation of antiderivatives and Riemann integrals.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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