Subject description - BD6B01MAA
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Explanatory Notes
Instructions
| BD6B01MAA |
Mathematics Analysis |
| Roles: | P |
Extent of teaching: | 14KP+6KC |
| Department: | 13101 |
Language of teaching: | |
| Guarantors: | |
Completion: | Z,ZK |
| Lecturers: | |
Credits: | 5 |
| Tutors: | |
Semester: | Z |
Web page:
https://math.fel.cvut.cz/en/people/zhukavet/b6b01maa.html
Anotation:
This course is an introduction to differential and integral calculus. It covers basic properties of functions, limits of functions, derivative and its applications (graphing, Taylor polynomial) and definite/indefinite integral with its applications, sequences and series.
Course outlines:
| 1. | | Introduction to calculus. |
| 2. | | Real numbers, basic mathematical terminology. |
| 3. | | Functions, elementary functions. |
| 4. | | Limit of a function, continuity. |
| 5. | | Derivative, properties and interpretations. |
| 6. | | L'Hospital's rule, the Taylor polynomial. |
| 7. | | Extrema of functions. Graph sketching. |
| 8. | | Indefinite integral (antiderivative), basic methods. |
| 9. | | Integrating rational functions using partial fractions. |
| 10. | | Definite integral, properties and evaluation. |
| 11. | | Improper integral, applications of integral. |
| 12. | | Sequences. |
| 13. | | Series. |
Exercises outline:
Practical classes follow lectures thematically. While on lectures, the focus is on understanding of notions and on justifications of validity of claims, in exercises students learn to solve routine problems.
| 1. | | Introduction to calculus. |
| 2. | | Real numbers, basic mathematical terminology. |
| 3. | | Functions, elementary functions. |
| 4. | | Limit of a function, continuity. |
| 5. | | Derivative, properties and interpretations. |
| 6. | | L'Hospital's rule, the Taylor polynomial. |
| 7. | | Extrema of functions. Graph sketching. |
| 8. | | Indefinite integral (antiderivative), basic methods. |
| 9. | | Integrating rational functions using partial fractions. |
| 10. | | Definite integral, properties and evaluation. |
| 11. | | Improper integral, applications of integral. |
| 12. | | Sequences. |
| 13. | | Series. |
Literature:
| 1. | | M. Demlová, J. Hamhalter: Calculus I. ČVUT Praha, 1994 |
| 2. | | P. Pták: Calculus II. ČVUT Praha, 1997. |
| 3. | | Math Tutor http://math.feld.cvut.cz/mt |
Requirements:
High-school mathematics.
Subject is included into these academic programs:
| Page updated 25.4.2024 05:52:00, 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) |