Multivariable Calculus

Relations:

The course F7ABBFVP can be graded only after the course F7ABBITP has been successfully completed.

Course guarantor:

Lecturer:

Tutor:

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, Dirichlets theorem, Fubinis 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, Dirichlets theorem, Fubinis 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:

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

Time-table for winter semester 2025/2026:

Time-table is not available yet

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans:

• Prospectus - bakalářský (!)
• Biomedical Technology (compulsory elective course)
• Biomedical Technology (compulsory elective course)