Course content

The course provides an introduction to basic theory and methods in mathematics that are relevant for all engineering disciplines.

The mathematical topics in the course are:

Linear algebra

• Solving systems of equations
• Simple matrix calculus and linear transformations
• Vector space, subspace, basis, linear dependence
• Eigenvalues and eigenvectors

Calculus

• Differentiation and integration
• 1st order ordinary differential equations
• 2nd order ordinary differential equations and systems of 1st order ordinary differential equations

Complex numbers

• Cartesian and polar form
• Applications to eigenvalues and 2nd order differential equations

Learning outcome

Knowledge

The candidate has good knowledge of

• basic concepts from linear algebra such as linear system, matrix, basis, vector space, eigenvector and eigenvalue.
• linear transformations and their representations in matrix form.
• basic concepts from calculus and differential equations such as the derivative of a function, integral, solution of a differential equation, linear, first and second order differential equations.
• the correspondence between second-order differential equations and systems of first-order differential equations.
• complex numbers and some representations thereof, and how they can be used in applied mathematics.
• some engineering applications of mathematics

Skills

The candidate

• can solve simple problems in linear algebra analytically, a.o. solve systems of linear equations and find eigenvalues ​​and eigenvectors of smaller matrices.
• can interpret solutions of linear systems of equations geometrically for 2x2 and 3x3 matrices.
• can represent linear transformations both geometrically and algebraically.
• can solve systems of linear equations and find eigenvalues ​​and eigenvectors, including complex eigenvalues, using digital tools.
• can solve 1st order separable differential equations and 2nd order linear differential equations with constant coefficients.
• can solve ordinary differential equations using digital tools, and can interpret results of numerical computations.

General competence

The candidate

• knows and can use mathematical symbols and formulas for communication in engineering.
• can assess own and other students' academic work, and give oral assessments in an academically correct and precise manner.
• knows and can apply mathematical methods to problems from own and adjacent subject areas.
• is familiar with applications of mathematical concepts and techniques in models that the candidate encounters within and outside the studies.

Learning methods and activities

Lectures, individual exercises and group work.

Compulsory assignments

The compulsory assignments consist of two parts:

• Compulsory exercises that are based on both analytical and numerical solution of problems and interpretation of the results. The assignments include tasks to be solved with the help of digital tools.
• Compulsory group work with focus on problems from the engineering profession.

Special conditions

Obligatory activities from previous semesters can be accepted by the institute.

Compulsory assignments

• Exercises

Specific conditions

Recommended previous knowledge

Similar to bachelor in engineering.

Course materials

Recommended course material will be announced at the start of the semester.

Credit reductions