Entry requirements

Calculus in one variable, algebra and linear algebra.

Aims

The course provides fundamental knowledge about real and vector valued functions of one and several variables - their local and global properties. Furthermore it gives training in mathematical modelling.

Content

Real and vector valued functions of one and several variables. Spacecurves: parametric representation, tangent. Partial derivatives: the chain rule, gradients, directional derivatives, differentials. The total derivative of vector fields, functional determinants. Taylors formula. Optimisation problems. Double and triple integrals, variable substitution, applications. Line integrals, the theorem of Green and exact differentials in the plane.

Instruction

Lectures and problem classes.

Assessment

Written exam at the end of the course. Compulsory tasks may be given during the course.