Mathematical Analysis 1
Mathematical Analysis 1 B0B01MA1A
Credits | 6 |
Semesters | Winter |
Completion | Assessment + Examination |
Language of teaching | Czech |
Extent of teaching | 4P+2S |
Annotation
This is an introductory course to differential and integral calculus of functions of one real 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. Series, convergence tests.
12. Introduction to differential equations.
13. Other topics of mathematical analysis.
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. Series, convergence tests.
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. Series, convergence tests.
12. Introduction to differential equations.
13. Other topics of mathematical analysis.
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. Series, convergence tests.
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
For information, see https://moodle.fel.cvut.cz/mod/page/view.php?id=196939 (in Czech).
Responsible for the data validity:
Study Information System (KOS)