|
Lecturer(s)
|
-
Pátíková Zuzana, doc. Mgr. Ph.D.
-
Kolařík Miroslav, doc. RNDr. Ph.D.
|
|
Course content
|
- Indefinite integral and the methods of integrating - antiderivative of the function, indefinite integral, integration by parts, substitution method, decomposition into partial fractions, integration of rational functions, trigonometric substitution. - Definite integral - basic properties, integration by parts and substitution method, geometrical applications, physical applications. - The n-dimensional Euclidean point-vector space En, the real function of several variables. - Limit of a function of n real variables, partial derivatives, total differential and differentiability of a function, tangent plane and normal line of a surface. - Local, constrained and global extremes of function. - Implicitly defined functions - Introduction to the integral of vector function
|
|
Learning activities and teaching methods
|
|
unspecified
|
| prerequisite |
|---|
| Knowledge |
|---|
| Student ovládá odborné znalosti nabyté v předmětu Matematika 1. |
| Student ovládá odborné znalosti nabyté v předmětu Matematika 1. |
| Skills |
|---|
| Student ovládá odborné dovednosti získané v předmětu Matematika 1. |
| Student ovládá odborné dovednosti získané v předmětu Matematika 1. |
| learning outcomes |
|---|
| Knowledge |
|---|
| Explain what a primitive function is to a given function. |
| Explain what a primitive function is to a given function. |
| Formulate the Newton-Leibniz formula. |
| Formulate the Newton-Leibniz formula. |
| List what a certain integral can be used for. |
| List what a certain integral can be used for. |
| Describe the geometric meaning of the partial derivatives of a function of two variables at a point. |
| Describe the geometric meaning of the partial derivatives of a function of two variables at a point. |
| Explain the meaning of gradient at a point. |
| Explain the meaning of gradient at a point. |
| Describe the process of finding local extrema of a function of two variables. |
| Describe the process of finding local extrema of a function of two variables. |
| Skills |
|---|
| Integrate using integration formulas and integrand modifications. |
| Integrate using integration formulas and integrand modifications. |
| Apply integration methods per partes and substitution. |
| Apply integration methods per partes and substitution. |
| Decompose a rational function into partial fractions. |
| Decompose a rational function into partial fractions. |
| Using a definite integral, calculate the area content of bounded graphs of elementary functions. |
| Using a definite integral, calculate the area content of bounded graphs of elementary functions. |
| Describe simple integration areas (square, rectangle, triangle, area between graphs of elementary functions) using inequalities. |
| Describe simple integration areas (square, rectangle, triangle, area between graphs of elementary functions) using inequalities. |
| Calculate the double integral in Cartesian coordinates. |
| Calculate the double integral in Cartesian coordinates. |
| Convert the appropriate double integral to polar coordinates and integrate. |
| Convert the appropriate double integral to polar coordinates and integrate. |
| Compute partial derivatives of functions of two variables. |
| Compute partial derivatives of functions of two variables. |
| Construct the equation of the tangent plane to the graph of a function of two variables at a point. |
| Construct the equation of the tangent plane to the graph of a function of two variables at a point. |
| Find the stationary points of the function of two variables and use the Sylvester decision criterion to decide on the type of local extremum. |
| Find the stationary points of the function of two variables and use the Sylvester decision criterion to decide on the type of local extremum. |
| Find global extrema on a compact set. |
| Find global extrema on a compact set. |
| teaching methods |
|---|
| Knowledge |
|---|
| Lecturing |
| Lecturing |
| assessment methods |
|---|
| Grade (Using a grade system) |
| Grade (Using a grade system) |
| Written examination |
| Written examination |
|
Recommended literature
|
-
Anton H., Bivens I., Davis S. Calculus. Wiley, 2012. ISBN 978-0-470-64769-1.
-
Ostravský, J. Diferenciální počet funkce více proměnných. Nekonečné číselné řady. Zlín : UTB, 2007. ISBN 978-80-7318-567-1.
-
Ostravský J., Polášek V. Diferenciální a integrální počet funkce jedné proměnné: vybrané statě. Zlín, 2011. ISBN 978-80-7454-124-7.
-
Riley, K.F. a kol. Mathematical Methods for Physics and Engineering. Cambridge University Press, 2015. ISBN 100521679710.
|