Course content

Complex numbers. Euler's formula. The fundamental theorem of algebra.

Systems of linear equations. Gauss elimination. Existence, uniqueness and parametrization of solutions.

Vector equations. Linear span. Matrices. LU-factorization. Matrix algebra. Identity matrices. Inverse matrices.

Linear independence. Determinants. Properties of determinants. Vector space. Row, column and null space of a matrix. Linear transformation. Isomorphism.

Projection of a vector. Orthogonal projection. Inner product. Inner product space. Cauchy-Schwarz' inequality. Orthogonal basis. Gram-Schmidt's method.

Eigenvalues. Eigenvectors. Diagonalization.

Numerical linear algebra. Newton's method. Gauss elimination with pivoting. Error propagation. Vector and matrix norms. Condition number. Iterative methods.

Systems of first-order differential equations. Second order differential equations. Error analysis. Runge-Kutta methods. Stiff differential equations.

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 concerning solving systems of linear equations and systems of first-order differential equations. The student understands and can apply basic concepts and methods concerning linear systems of equations and matrices. The student has knowledge about algorithmic thinking in order to understand and apply basic numerical methods for solving systems of linear equations and 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 various 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 tasks

Recommended previous knowledge

Mathematics R2 from upper secondary school, or equivalent knowledge.

Course materials

To be announced at the start of the semester.

Credit reductions