Course content

Sequences. Completeness property for real numbers. Convergence of sequences (both pointwise and uniform convergence). Cardinality and countability. The concept of a limit.

Properties and theorems related to continuous functions of one variabel: Continuity, the intermediate value theorem and the extreme value theorem.

Differentiation of functions of one variable. Rules of differentiation. The mean value theorem. Optimization of functions (identifying maxima and minima).

Approximation of functions by Taylor polynomials. Taylor's theorem.

Transcendent functions. Inverse functions. Exponential functions and logarithms. Trigonometric functions. Inverse trigonometric functions.

The definite integral of functions of one variable. Riemann sums. The fundamental theorem of analysis. Analytical and numerical integration techniques. The area of surfaces of revolution. The volum of solids of revolution.

Series. Tests for convergence for series. Alternating series. Power series. Taylor series.

Separable and linear differential equations. Existence and uniqueness of solutions. Analytical and numerical solution methods. Convergence and error analysis. 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 one-variable mathematical analysis related to sequences, continuity, differentiation, integration, Taylor polynomials and convergence of sequences. The student has knowledge about algorithmic thinking in order to understand and apply basic numerical methods for integration and for solving non-linear equations, linear systems of 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