Mathematics 1: Calculus and Linear Algebra

The course is a deepening and continuation of subject matter on functions and vectors from upper secondary school and it forms the foundation for the other mathematics courses in the Master of Technology study programmes.

Number sets (from natural to complex numbers). The limit concept, convergence of sequences, completeness of the real numbers. Properties and theorems connected to functions of one real variable: Continuity, the Intermediate-Value Theorem, the Mean-Value Theorem. Optimisation of functions (max/min problems). Approximation of functions with Taylor polynomials.

Systems of linear equations. Linear dependence and independence, and dimensional analysis (in R3). Gauss elimination. Matrices and determinants. Eigenvalues and eigenvectors.

The derivative of functions of one real variable. Composite functions. Differentiation rules. The definite integral of functions of one real variable. Riemann sums. The Fundamental Theorem of Calculus. Improper integrals. Analytical and numerical integration methods

Iterative methods. Convergence and error analysis.

Separable and linear differential equations. Existence and uniqueness of solutions. Analytical and numerical solution methods. Convergence and error analysis.

Examples of mathematical modelling and applications in science and technology.

The student understands and can apply basic concepts, results and methods from one-variable mathematical analysis related to limits, continuity, differentiation, integration, convergence of sequences, and Taylor polynomials. 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 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.

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.