## Tools and Techniques for Simulation and Optimisation, 5hp

## General aims of the course

The aim of this course is to introduce important concepts and techniques of modern numerical methods in Scientific Computing, comprising fundamental numerical linear algebra, numerical methods for ordinary differential equations, and optimization.

The course modules are devoted to analysis and implementation issues related to problems originating from various practical applications. Following those modules, the participants will obtain an overview of a selection of important methods and techniques. This knowledge will in turn act as a guideline when choosing appropriate techniques in real-life situations.

## Course contents

The course is partitioned into three modules:

- Fundamental numerical linear algebra.
- Numerical methods for ordinary differential equations.
- Optimization for continuous problems.

## Learning outcomes

After completing the course you should be able to…

- … explain the concepts of problem conditioning, convergence, and numerical stability.
- … define basic concepts in numerical linear algebra.
- … use modern software to solve basic problems in numerical linear algebra.
- … numerically solve ordinary differential equations using an applicable method.
- … discuss fundamental optimization methods including strengths and weaknesses.
- … reformulate a given problem as a mathematical optimization problem and solve it using a suitable optimization method.

## Examination

The examination is performed using a number of homework assignments.

## Prerequisites

Introductory linear algebra and vector calculus.

## Course schedule

Week N-1 (preparatory work at home)

Week N (lectures in Umeå)

Week N+1 (homework)

## Course responsible

Eddie Wadbro: eddie.wadbro@umu.se