Subject description - A8B01MC1
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Explanatory Notes
Instructions
| A8B01MC1 | Mathematics-Calculus1 | ||
|---|---|---|---|
| Roles: | P | Extent of teaching: | 4P+2S |
| Department: | 13101 | Language of teaching: | CS |
| Guarantors: | Tkadlec J. | Completion: | Z,ZK |
| Lecturers: | Křepela M. | Credits: | 7 |
| Tutors: | Křepela M., Tkadlec J. | Semester: | Z |
Web page:
https://moodle.fel.cvut.cz/courses/A8B01MC1Anotation:
The aim of the course is to introduce students to basics of differential and integral calculus of functions of one variable.Course outlines:
| 1. | Elementary functions. Limit and continuity of functions. | |
| 2. | Derivative of functions, its properties and applications. | |
| 3. | Mean value theorem. L'Hospital's rule. | |
| 4. | Limit of sequences. 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. | Numerical evaluation of definite integral. Application to calculation of areas, volumes and lengths. | |
| 10. | Improper integral. | |
| 11. | Differential equations - formulation of the problem. Separation of variables. | |
| 12. | First order linear differential equations (variation of parameter). | |
| 13. | Applications. Numerical aspects. | |
| 14. | Reserve. |
Exercises outline:
| 1. | Elementary functions. Limit and continuity of functions. | |
| 2. | Derivative of functions, its properties and applications. | |
| 3. | Mean value theorem. L'Hospital's rule. | |
| 4. | Limit of sequences. 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. | Numerical evaluation of definite integral. Application to calculation of areas, volumes and lengths. | |
| 10. | Improper integral. | |
| 11. | Differential equations - formulation of the problem. Separation of variables. | |
| 12. | First order linear differential equations (variation of parameter). | |
| 13. | Applications. Numerical aspects. | |
| 14. | Reserve. |
Literature:
| 1. | M. Demlová, J. Hamhalter: Calculus I. ČVUT Praha, 1994 | |
| 2. | P. Pták: Calculus II. ČVUT Praha, 1997. |
Requirements:
See web page.Keywords:
limits, derivatives, integrals, series Subject is included into these academic programs:| Program | Branch | Role | Recommended semester |
| BPOES_2020 | Common courses | P | 1 |
| BPOES | Common courses | P | 1 |
| Page updated 19.4.2024 17:54:04, semester: Z,L/2023-4, Z/2024-5, Send comments about the content to the Administrators of the Academic Programs | Proposal and Realization: I. Halaška (K336), J. Novák (K336) |