Moodle FEL ČVUT
Calculus 1
B241 - Zimní 2024/2025
Calculus 1 - BE5B01MA1
| Kredity | 7 |
| Semestry | zimní |
| Zakončení | zápočet a zkouška |
| Jazyk výuky | angličtina |
| Rozsah výuky | 4P+2S |
Anotace
It is an introductory course to calculus of functions of one variable. It starts with limit and continuity of functions, derivative and its geometrical meaning and properties, graphing of functions. Then it covers indefinite integral, basic integration methods and integrating rational functions, definite integral and its applications. It concludes with introduction to Taylor series.
Cíle studia
None
Osnovy přednášek
1. The real line, elementary functions and their graphs, shifting and scaling.
2. Limits and continuity, tangent, velocity, rate of change.
3. Derivative of functions, properties and applications.
4. Mean value theorem, L'Hospital's rule.
5. Higher derivatives, Taylor polynomial.
6. Local and global extrema, graphing of functions.
7. Indefinite integral, basic integration methods.
8. Integration of rational functions, more techniques of integration.
9. Definite integral, definition and properties, Fundamental Theorems of Calculus.
10. Improper integrals, tests for convergence. Mean value Theorem for integrals, applications.
11. Sequences of real numbers, numerical series, tests for convergence.
12. Power series, uniform convergence, the Weierstrass test.
13. Taylor and Maclaurin series.
2. Limits and continuity, tangent, velocity, rate of change.
3. Derivative of functions, properties and applications.
4. Mean value theorem, L'Hospital's rule.
5. Higher derivatives, Taylor polynomial.
6. Local and global extrema, graphing of functions.
7. Indefinite integral, basic integration methods.
8. Integration of rational functions, more techniques of integration.
9. Definite integral, definition and properties, Fundamental Theorems of Calculus.
10. Improper integrals, tests for convergence. Mean value Theorem for integrals, applications.
11. Sequences of real numbers, numerical series, tests for convergence.
12. Power series, uniform convergence, the Weierstrass test.
13. Taylor and Maclaurin series.
Osnovy cvičení
1. The real line, elementary functions and their graphs, shifting and scaling.
2. Limits and continuity, tangent, velocity, rate of change.
3. Derivative of functions, properties and applications.
4. Mean value theorem, L'Hospital's rule.
5. Higher derivatives, Taylor polynomial.
6. Local and global extrema, graphing of functions.
7. Indefinite integral, basic integration methods.
8. Integration of rational functions, more techniques of integration.
9. Definite integral, definition and properties, Fundamental Theorems of Calculus.
10. Improper integrals, tests for convergence. Mean value Theorem for integrals, applications.
11. Sequences of real numbers, numerical series, tests for convergence.
12. Power series, uniform convergence, the Weierstrass test.
13. Taylor and Maclaurin series.
2. Limits and continuity, tangent, velocity, rate of change.
3. Derivative of functions, properties and applications.
4. Mean value theorem, L'Hospital's rule.
5. Higher derivatives, Taylor polynomial.
6. Local and global extrema, graphing of functions.
7. Indefinite integral, basic integration methods.
8. Integration of rational functions, more techniques of integration.
9. Definite integral, definition and properties, Fundamental Theorems of Calculus.
10. Improper integrals, tests for convergence. Mean value Theorem for integrals, applications.
11. Sequences of real numbers, numerical series, tests for convergence.
12. Power series, uniform convergence, the Weierstrass test.
13. Taylor and Maclaurin series.
Literatura
1. M. Demlová, J. Hamhalter: Calculus I. ČVUT Praha, 1994
2. P. Pták: Calculus II. ČVUT Praha, 1997.
https://math.fel.cvut.cz/en/people/vivipaol/BE5B01MA1.html
2. P. Pták: Calculus II. ČVUT Praha, 1997.
https://math.fel.cvut.cz/en/people/vivipaol/BE5B01MA1.html
Požadavky
https://math.fel.cvut.cz/en/people/vivipaol/MA12015.pdf