(Created 2010-07-25.)

APPLIED MATHEMATICS - LINEAR SYSTEMS | FMAF10 |

**Aim**

The aim of the course is to treat some mathematical concepts and methods above the basic level that are important for further studies within e.g. mechanics, solid mechanics, control theory, electrical engineering and for further professional activities.

*Knowledge and understanding*

For a passing grade the student must

be familiar with the Laplace transform and its significance in connection with input/output relations and solving differential equations, and be well versed in handling simple transform tables.

have good knowledge of such matrix algebra which is the foundation of eigenvalue problems and of solving systems of differential equations.

*Skills and abilities*

For a passing grade the student must

be able to show ability to use the concepts in connection with problem solving.

with proper terminology, suitable notation, well structured and with clear logic be able to explain the solution to a problem.

**Contents***Linear systems:* Mathematical models of linear, time invariant systems. Transfer function. Step response and impulse response. The frequency function.

*The Laplace transform:* Step and impulse functions. Computational rules for the two-sided Laplace transform. Inverse transforms, in particular of rational functions. Use of transform tables. Convolution.

*Matrix algebra:* Eigenvalues and eigenvectors. Diagonalization, in particular of symmetric matrices. Quadratic forms, diagonalization and classification. Systems of differential equations: solution by diagonalization, solution using exponential matrix.

**Literature**

Spanne, S. & Sparr, A.: Föreläsningar i Tillämpad matematik, Lineära system. KF-Sigma.