# ADA501 Mathematical modeling and simulation

## Course description for academic year 2023/2024

### Contents and structure

This is an introductory course in mathematical modeling and simulation for engineers. It explores the lifecycle of mathematical modeling in engineering: how to start from a description of a phenomenon, problem, or process and reformulate it to a well-posed mathematical problem, carry out appropriate mathematical and computational analysis, estimate and optimize parameters,obtain a solution using computational and numerical methods, evaluate the solution, and then present the results. The students will get familiarized with both ordinary and partial differential equations and will be introduced to traditional numerical solution strategies for these equations.

Through multiple examples of modeling and simulation of a variety of systems and processes related to engineering, the course aims to provide a mental framework that will be useful both for further studies and for a future career in engineering.

### Learning Outcome

Knowledge:

The student

• can explain what a mathematical model is, and the main steps involved in their construction.
• can explain the role of mathematical modeling as a fundamental method in enginerring.
• can use mathematical modeling and simulation to study a range of phenomena and processes arising in engineering.
• can estimate model parameters in engineering problems from given data.
• can explain how differential equations are used in mathematical modeling.
• can explain the role of numerical and computational methods in the solution of differential equations.
• is knowledgable about the limitations of mathematical models and the methods used to verify and identify their applicability to concrete problems

Skills:

The student

• knows how to formulate and analyze simple, but realistic systems and processes from engineering into a mathematical framework, deriving actionable and useful mathematical models.
• knows how to formulate a problem as a differential equation and the principles behind solving these equations numerically.
• can use simulations to study the behavior of such models and verify their ability to capture the phenomena under study.
• can explain the features characterising a good model.

General competency:

The student

• can apply the methods covered by the course to new areas.
• can work efficiently with others.
• can explain problems, analyzes and conclusions related to mathematical modeling to peers, both in writing and orally.

None

### Teaching methods

Lectures, workshops, group presentations and group supervision related to course project work.

### Compulsory learning activities

Three obligatory assignments, of which two are group assignments.

In order to take the examinations, the assignments must be approved within the specified deadlines. Approved assignments are valid for two semesters.

### Assessment

Part 1: Written project group work, report of 3000-4000 words, accounting for 50% of the final grade. If the project group work is not passed, an improved version of the same problem can be submitted in the following semester. Afterwards, a different project work must be done.

Part 2: Written examination, 4 hours, accounting for 50% of the final grade.

Grade scale A-F, where F is fail. Both elements must be passed to pass the course and obtain a final grade. When only one element is failed, this element can be taken up alone in the following semester. Afterwards, both elements must be redone.

### Examination support material

For written project group work: all support materials are permitted

For written examination: simple calculator and all physical printed and written aids.