Calculus in several variables
7.5 ECTS creditsMain 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鈥恈ycle 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)
More information
- Start Spring 2025
- Mode of study Campus
- Language Swedish
- Course code MAGA54
- Application code KAU-43790
- Study pace 50% (Day)
- Study period week 14鈥23
- Schedule
- Introductory Information
- Reading list