Course content

The course builds on TMA4400 and TMA4411 and further develops topics from these courses. The course continues the study of multivariable calculus. In addition, it discusses methods for the approximation of functions.

Space curves; vector functions; Newton's method in several variables; chain rule; double and triple integrals; curve and surface integrals; vector calculus; vector fields; Green's, Stokes', and Gauss' theorems; interpolation and approximation; least squares method.

Learning outcome

The student understands and can apply basic notions, results, and methods from multivariable calculus connected to derivation and integration. The student can apply different analytical approaches for the computation of integrals of functions of several variables, and understands the connection between volume and boundary integrals in different situations.

The student is familiar with different methods for the approximation of functions, can use them for the analytic computation of approximations in simple cases, and is familiar with the implementation of the methods. The student is aware of the limitations of these methods regarding applications and the possible precision of the approximations.

The student can use analytical and computational methods to formulate, model, and solve simple technological problems relevant to their study programme.

The course will primarily contribute to competence area K1, show specialist knowledge and a professionally grounded perspective. It will also contribute to competence area K2, analyzing engineering problems in collaboration with the individual study programmes that the course serves.

Learning methods and activities

Lectures and compulsory exercises. The number of exercises that must be approved will be stated at the start of the semester on the course's website. The course or parts of it may be taught in English.

Compulsory assignments

• Obligatoric exercises

Recommended previous knowledge

TMA4400 - Mathematics 1, TMA4411 - Mathematics 2B, or equivalent.

Course materials

Will be announced at the start of the semester.

Credit reductions