Multivariable Calculus
Code | Completion | Credits | Range | Language |
---|---|---|---|---|
F7PBBFVP | KZ | 2 | 1P+1C | Czech |
- Grading of the course requires grading of the following courses:
- Integral Calculus (F7PBBITP)
- 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 2022/2023:
-
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 Wed Thu Fri - Time-table for summer semester 2022/2023:
- Time-table is not available yet
- The course is a part of the following study plans:
-
- Biomedical Technology (compulsory elective course)