### Mathematical Analysis 1

#### Mathematical Analysis 1 - BD5B01MA1

 Credits 8 Semesters Both Completion Assessment + Examination Language of teaching Czech Extent of teaching 28KP+6KC
Annotation
The aim of the course is to introduce students to basics of differential and integral calculus of functions of one variable.
Study targets
The aim of the course is to introduce students to basics of differential and integral calculus of functions of one variable.
Course outlines
1.Real numbers. Elementary functions.
2. Limit and continuity of functions.
3. Derivative of functions, its properties and applications.
4. Mean value theorem. L'Hospital's rule, Taylor polynomial.
5. Local and global extrema and graphing functions.
6. Indefinite integral, basic integration methods.
7. Integration of rational and other types of functions.
8. Definite integral (using sums). Newton-Leibniz formula.
9. Improper integral. Application of integrals.
10. Sequences and their limits.
11. Rows, criteria of convergence.
12. Introduction to differential equations.
13. Other topics of mathematical analysis.
Exercises outlines
1.Real numbers. Elementary functions.
2. Limit and continuity of functions.
3. Derivative of functions, its properties and applications.
4. Mean value theorem. L'Hospital's rule, Taylor polynomial.
5. Local and global extrema and graphing functions.
6. Indefinite integral, basic integration methods.
7. Integration of rational and other types of functions.
8. Definite integral (using sums). Newton-Leibniz formula.
9. Improper integral. Application of integrals.
10. Sequences and their limits.
11. Rows, criteria of convergence.
12. Introduction to differential equations.
13. Other topics of mathematical analysis.
Literature
[1] J. Stewart, Single variable calculus, Seventh Edition, Brooks/Cole, 2012, ISBN 0538497831.
Requirements