# Calculus in several variables

7.5 ECTS credits

Main course components:

- Basic topological concepts: open, closed and compact sets.

- Functions of several variables with limits and continuity, partial derivatives, the chain rule, directional derivatives and gradients, tangent planes, Jacobian matrices and Jacobian determinants.

- Coordinate transformations, simple partial differential equations.

- Taylor polynomials in several variables.

- Extreme values: classifying critical points, local and global extreme values, the method of Lagrange multipliers.

- Double and triple integrals: iterated integration, change of variables with polar, cylindrical and spherical coordinates, generalized integrals

- Geometrical and physical applications: area of curved surface, volume, mass and centre of mass

- Vector fields, conservative vector fields, potentials

- Divergence and rotation operators, nabla operator

- Line integrals, surface integrals, flux integrals

- Green's formula, Gauss' divergence theorem, Stokes' theorem.

- Basic topological concepts: open, closed and compact sets.

- Functions of several variables with limits and continuity, partial derivatives, the chain rule, directional derivatives and gradients, tangent planes, Jacobian matrices and Jacobian determinants.

- Coordinate transformations, simple partial differential equations.

- Taylor polynomials in several variables.

- Extreme values: classifying critical points, local and global extreme values, the method of Lagrange multipliers.

- Double and triple integrals: iterated integration, change of variables with polar, cylindrical and spherical coordinates, generalized integrals

- Geometrical and physical applications: area of curved surface, volume, mass and centre of mass

- Vector fields, conservative vector fields, potentials

- Divergence and rotation operators, nabla operator

- Line integrals, surface integrals, flux integrals

- Green's formula, Gauss' divergence theorem, Stokes' theorem.

Progressive specialisation:
G1F (has less than 60 credits in first‐cycle course/s as entry requirements)

Education level:
Undergraduate level

Admission requirements:
Foundation course in Mathematics 7.5 ECTS cr., Calculus and Geometry, 7.5 ECTS cr, and Linear Algebra 7.5 ECTS cr each, or equivalent.

Selection:

Selection is usually based on your grade point average from upper secondary school or the number of credit points from previous university studies, or both.

### This course is included in the following programme

- Bachelor Programme in Physics (studied during year 1)
- Mathematics Programme (studied during year 1)
- Master of Science in Computer Engineering (studied during year 2)
- Master of Science in Energy and Environmental Engineering (studied during year 1)
- Master of Science in Industrial Engineering and Management (studied during year 1)
- Master of Science in Chemical Engineering (studied during year 1)
- Master of Science in Mechanical Engineering (studied during year 1)
- Master of Science in Engineering Physics (studied during year 1)