Single-Course Engelsk 5 ECTS

# Mathematical Modeling

## Overall Course Objectives

Mathematical modeling is a prerequisite in solving the majority of technical problems. A typical solution is found by first formulating a mathematical model that is implemented on a computer, and after that a lab scale experiment is set up and finally a real world solution is made. The ability to formulate a relevant mathematical model, which can be implemented in a computer and provide useful information is a fundamental prerequisite for modern engineering. In this course the student will get tools for setting up a mathematical model, carry out simulations and calculations on these models, and perform a critical analysis and report the obtained results.

See course description in Danish

Learning Objectives

• Apply a mathematical model to solve a problem
• Explain the components of a mathematical model
• Judge area of validity of a mathematical model
• Use statistics to summarize the obtained results
• Implement numerical algorithms using Matlab or Python
• Set up test scenarios and collect data
• Explain the model parameter’s influence on the model
• Interpret the calculated results of the model
• Visualize data and results graphically
• Evaluate the relevance of the results for the analyzed problem
• Write a stringent and structured report that precisely describes the model and analysis of the calculated results

Course Content

The main content of the course is to solve specific cases with associated problems. For each case a problem has to be analyzed, the mathematical model must be described and implemented on a computer, and calculations and simulations must be done, which illustrates the relevance of the model. All of this has to be reported in a structured manner. The methods will fall within discrete mathematics, image analysis, differential equations, materials science, operations research, and scientific computing. The course include peer grading of other students reports, which is a prerequisite for being examined

Recommended prerequisites

01025/01035/02601/02403/02402/02002/02525/02631/10018/10022, Knowledge of mathematical analysis, linear algebra and numerical analysis. Fundamental physics including mechanics. Knowledge of statistics and Matlab or Python programming. It will be an advantage to have knowledge of image analysis.

Teaching Method

Lectures, exercises and reports

Faculty

Remarks

The course is a prerequisite for the following advanced courses: 02610 Optimization and datafitting, 02614 High performance computing, 02616 Large-scale modeling, 02623 Finite element methods for partial differential equations, 02685 Scientific computing for differential equations. The course is reserved for students from Mathematics and Technology and General Engineering, and other students are welcome if there are available seats.

See course in the course database.

## Registration

Language Engelsk 13 weeks Compute DTU Lyngby Campus Management 02526 Bachelor Week 6 Week 20 Tues 8-12
Price 9.250,00 DKK