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F7ABBFVP - Multivariable Calculus

Code Completion Credits Range Language
F7ABBFVP KZ 2 1P+1C English
Grading of the course requires grading of the following courses:
Integral Calculus (F7ABBITP)
Lecturer:
Petr Maršálek (guarantor)
Tutor:
Petr Maršálek (guarantor)
Supervisor:
Department of Natural Sciences
Synopsis:
Requirements:
Syllabus of lectures:

1. Multi variable function, limit, continuity, partial derivative, higher order partial derivative, directional derivative, gradient.

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

3. Local and constrained extrema, Lagrange multipliers.

4. Double integrals, substitution in double integral, Jacobian, Dirichlet’s theorem, Fubini’s theorem.

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

6. Curve integrals of the first and second kind.

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

Syllabus of tutorials:

1. Multi variable function, limit, continuity, partial derivative, higher order partial derivative, directional derivative, gradient.

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

3. Local and constrained extrema, Lagrange multipliers.

4. Double integrals, substitution in double integral, Jacobian, Dirichlet’s theorem, Fubini’s theorem.

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

6. Curve integrals of the first and second kind.

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

Study Objective:
Study materials:
Note:
The course is a part of the following study plans:
Downloads:

Lectures - link: 

MULTIVARIABLE FUNCTIONS -LECTURES : https://harm.fbmi.cvut.cz/B221/F7ABBFVP/lec

Exercises - link: 

MULTIVARIABLE FUNCTIONS - SEMINARS : https://harm.fbmi.cvut.cz/B221/F7ABBLAD/tut