Course content

The course is based on TMA4400 and develops topics from this course further. In addition, various forms of infinite series, methods for approximating functions and integral transforms are treated.

General vector spaces and linear transformations. Subspaces. Linear dependence and independence, and dimensional analysis in Rn and in general vector spaces. Basis. Kernel and range. Rank of matrices. Projection and orthogonalisation. Orthogonal functions. Inner product.

Linear systems of first-order differential equations. Numerical methods for ordinary differential equations. Integral transforms. The Delta function.

Series and improper integrals. Convergence tests. Approximation of functions. Taylor polynomials and Taylor series. Trigonometric polynomials and Fourier series. Uniform convergence.

Examples of mathematical modelling and applications in science and technology.

Learning outcome

The student understands and can apply basic concepts, results and methods from linear algebra in Euclidian spaces. The student understands and can apply basic concepts and methods concerning ordinary differential equations and series, and can determine whether a series converges or not. The student has knowledge about integral transforms and about basic properties of Fourier series and can approximate given functions with polynomials or trigonometric functions.

The student has knowledge about algorithmic thinking in order to understand and apply basic numerical methods for solving ordinary differential equations, including systems of ordinary differential equations. The student can analyse such methods with regard to applicability and precision.

The student is familiar with the use of numerical methods in a programming language and understands the possibilities and limitations of the various methods in relation to the 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, analysing engineering problems, in collaboration with the individual study programmes that the subject 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 will be taught in Norwegian.

Compulsory assignments

• Compulsory exercises

Recommended previous knowledge

TMA4400 - Mathematics 1: Calculus and Linear Algebra, or equivalent.

Course materials

Stated at the start of the semester.

Credit reductions