Course content

The course builds on TMA4400 and TMA4422 and further develops topics from these courses.

Introduction into methods for matrix and tensor factorisation. Singular value decomposition (SVD), tensors. Introduction to multivariable calculus: Space curves and vector functions. Partial derivatives, gradient, and directional derivative. Extremal values for functions of several variables. Continuous and discrete Fourier transform. Fourier series and FFT. Interpolation and approximation of functions; splines, Bézier curves, least squares method. Partial differential equations: finite differences for the solution of differential equations. Introduction to computational tools with examples.

Learning outcome

The student is familiar with matrix and tensor factorisation and understands how these approaches are used in order to simplify complex data sets.

The student understands and can apply basic notions, results, and methods from multivariable calculus, in particular differentiation.

The student understands basic notions, results, and methods from the theory of integral transforms and can apply them in different settings including function approximation.

The student has basic knowledge about the theory of partial differential equations and is familiar with analytic solution in simple cases. The student is familiar with the numerical solution of partial differential equations including the basic ideas of finite differences.

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 may be taught in English.

Compulsory assignments

• Obligatoric exercises

Recommended previous knowledge

TMA4400 - Mathematics 1, TMA4422 - Mathematics 3C, or equivalent.

Course materials

Will be announced at the start of the semester.

Credit reductions