Course content

The course is based on TMA4400, TMA4410, and TMA4420 and develops topics from these courses further. The course continues the study of functions of several variables, including vector valued functions. In addition, it discusses partial differential equations, and it provides an introduction into approximation of functions and the mathematical basis of machine learning.

Conical sections. Vector analysis: vector fields, Green's, Stokes', and Gauss' theorems. Partial differential equations and their analytical and numerical solution. Approximation of functions. Introduction into the mathematical basis of machine learning.

Examples of mathematical modeling and applications within science and technology.

Learning outcome

The student understands and can apply basic notions, results, and methods from multivariable calculus, including the main theorems of vector analysis. The student understands the connection between volume integrals and boundary integrals in different situations.

The student has basic knowledge about the theory of partial differential equations and is familiar with approaches to their analytic solution in simple cases. The students has knowledge about numerical methods for the solution of partial differential equations.

The student is familiar with different methods for the approximation of functions and is able to implement and use these methods. In addition, the student is able to analyse such methods in terms of their applicability and precision, and understands the possibilities and limitations of the methods regarding the different problems they are applied to.

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, TMA4410 - Mathematics 2A, TMA4420 - Mathematics 3A, or equivalent.

Course materials

Will be announced at the start of the semester.

Credit reductions