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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

Multivariable Calculus

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Code Completion Credits Range Language
F7PBBFVP KZ 2 1P+1C Czech

The course F7PBBFVP can be graded only after the course F7PBBITP has been successfully completed.

Garant předmětu:
Jana Urzová
Lecturer:
Jana Urzová
Tutor:
Jana Urzová
Supervisor:
Department of Natural Sciences
Synopsis:

The course is focused at elements of calculus in two and more variables and at real, complex and functional series.

Calculus in two variables: notion of a limit and continuity, partial derivative, differential and its applications. Derivative of a composed function, derivative of an implicit function. Higher order derivatives, local extremes. Constrained extremes, least squares method. Double and triple integrals, geometrical interpretation, Fubini theorem. Integration by substitution in double and triple integral.

Complex sequences, series of numbers. Convergence of complex series. Functional series and their convergence, power series. Taylor series. .

Requirements:

Credit condition - 70% presence, successful written test on 3. and 6. exercise. It is necessary to gain at least one half of maximum number of points.

Theme of 1. test: Domain of definition of two variable function, tangent plane, local extrema.

Theme of 2. test: Double and triple integrals, convergence of series.

Syllabus of lectures:

1. Domains of definition, limit of two variable function, partial derivative, direction derivative.

2. Total differential, tangent plane. Derivative of composed function, derivative of implicit function.

3. Extrema of function, 1. test.

4. Double integral, substitution, application.

5. Triple integral, substitution, application.

6. Curve and surface integral, 2. test.

7. Convergence of number and function series.

Syllabus of tutorials:

1. Domains of definition, limit of two variable function, partial derivative, direction derivative.

2. Total differential, tangent plane. Derivative of composed function, derivative of implicit function.

3. Extrema of function, 1. test.

4. Double integral, substitution, application.

5. Triple integral, substitution, application.

6. Curve and surface integral, 2. test.

7. Convergence of number and function series.

Study Objective:

To learn the elements of multivariable function calculus and of number and function series.

Study materials:

[1] http://mathworld.wolfram.com/topics/CalculusandAnalysis.html

Note:
Time-table for winter semester 2023/2024:
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
roomKL:B-430
Urzová J.
16:00–17:50
EVEN WEEK

(lecture parallel1)
Kladno FBMI
Učebna
roomKL:B-430
Urzová J.
18:00–19:50
EVEN WEEK

(lecture parallel1
parallel nr.1)

Kladno FBMI
Učebna
Wed
Thu
Fri
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-02-28
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet6178206.html