Multivariable Calculus

Vztahy:

The course 17ABBFVP can be graded only after the course 17ABBITP has been successfully completed.

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Natural Sciences

Synopsis:

The course is focused at elements of calculus in two and more variables.

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.

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.

Syllabus of lectures:

1. Multiple variable function, limit, continuity, partial derivative, higher order partial derivative, direction derivative, gradient.

2. Differential and its applications, tangent plane. Derivative of composed function, derivative of implicit function.

3. Local and constrained extrema, Lagrange multiplicators.

4. Double integrals, Dirichlet theorem, Fubini theorem, substitution in double integral, jacobian.

5. Triple integrals, substitution, spherical, cylindrical coordinates.

6. Curve integrals of the 1. and 2. kind.

7. Surface integrals, Green, Stokes and Gauss theorem.

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.

Study materials:

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

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Biomedical Technician - full time study in English (compulsory elective course)