CTU FEE Moodle
Introduction to Calculus
B232 - Summer 23/24
Introduction to Calculus - A0B01MA1
| Credits | 8 |
| Semesters | Winter |
| Completion | Assessment + Examination |
| Language of teaching | Czech |
| Extent of teaching | 3+3 |
Annotation
This is an introductory course to calculus of real functions of one variable. In the first part we study limits and continuity of functions, derivative and its geometrical meaning, graphing of functions. Then we define the indefinite integral, and discuss basic integration methods, the definite integral and its applications. We conclude with an introduction to Laplace transform and its use in solving differential equations.
Study targets
No data.
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.Laplace transform.
12.Basic properties of direct and inverse Laplace transform.
13.Using Laplace transform to solve differential equations.
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.Laplace transform.
12.Basic properties of direct and inverse Laplace transform.
13.Using Laplace transform to solve differential equations.
Exercises 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.Laplace transform.
12.Basic properties of direct and inverse Laplace transform.
13.Using Laplace transform to solve differential equations.
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.Laplace transform.
12.Basic properties of direct and inverse Laplace transform.
13.Using Laplace transform to solve differential equations.
Literature
1. M. Demlová, J. Hamhalter: Calculus I. ČVUT Praha, 1994
2. P. Pták: Calculus II. ČVUT Praha, 1997.
2. P. Pták: Calculus II. ČVUT Praha, 1997.
Requirements
In order to obtain the certificate of attendance,
students are required to actively participate in the laboratory class, hand in the assigned
homework and obtain a sufficient score during lab tests. Only students who obtain attendance certificate ("zapocet") are allowed to take the exam.
http://math.feld.cvut.cz/vivi/AE0B01MA12010.pdf
students are required to actively participate in the laboratory class, hand in the assigned
homework and obtain a sufficient score during lab tests. Only students who obtain attendance certificate ("zapocet") are allowed to take the exam.
http://math.feld.cvut.cz/vivi/AE0B01MA12010.pdf