Mathematics for engineering 1

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

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 differential equations, first and second order differential equations.
• the correspondence between second-order differential equations and systems of first-order differential equations.
• basic arithmetic’s with complex numbers, 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 differentiate and integrate functions.
• can solve simple equations containing complex numbers.
• can solve 1st order separable differential equations and 2nd order linear differential equations with constant coefficients.

General competence

The candidate

• knows and can use mathematical symbols and formulas for communication in engineering.
• 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.

Lectures, individual exercises and project work.

Compulsory assignments

The compulsory assignments consist of two parts:

• Compulsory exercises that test the students ability to find solution of problems and interpretate of the results. The assignments include tasks to be solved with the help of digital tools.
• Compulsory project work with focus on problems from the engineering profession.