## AEM 3101: Mathematical Modeling and Simulation in Aerospace Engineering

### Catalog Description

Syllabus

AEM 3101

Mathematical Modeling and Simulation in Aerospace Engineering

2 Credits

Catalog Description:

Mathematical modeling of engineering systems and numerical methods for their solution. Use of MATLAB. Focuses on systems found in aerospace engineering and mechanics.

http://www.aem.umn.edu/courses/aem3101/

Prerequisites by Topic:

1. Differential equations and linear algebra (Math 2373)

Text:

Amos Gilat and Vish Subramiam, Numerical Methods for Engineers and Scientists: An Introduction with Applications Using MATLAB,. Wiley

Format of Course:

2 Lectures per week

Computer Usage:

MATLAB

Course Objectives:

The aim of this course is to develop a broad understanding of the use of numerical methods for the solution of various types of problems that appear in aerospace engineering. MATLAB is used as a platform providing a programming language and many directly applicable numerical routines. Students gain insight into mathematical modeling through the analysis of example problems.

Course Outcomes:

1. Familiarity with MATLAB as an essential tool for numerical problem-solving.
2. An understanding of numerical methods for curve fitting.
3. An understanding of numerical methods for root finding.
4. An understanding of numerical methods for integration and differentiation.
5. An understanding of numerical methods for the simulation of ordinary differential equations.

Relationship of course to program objectives:

This course develops skills in using modern engineering tools, in particular MATLAB, and essential numerical methods applicable in many areas of aerospace engineering and mechanics. Students are likely to use MATLAB and numerical methods in several of their following classes.

Relationship of course to student outcomes:

This course supports the following student outcomes:

1.       An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics.

2.       An ability to apply the engineering design process to produce solutions that meet specified needs with consideration public health and safety, and global, cultural, social, environmental, economic, and other factors as appropriate to the discipline.

Outcome Measurement

This course is not used to directly measure any of the student outcomes.

Course Outline:

 Lecture (Hrs, approx.) Topics 6 Introduction; MATLAB & Data Presentation: Vectors, Matrices, Vector/Matrix Operations & Manipulations. Functions vs scripts. Making clear and compelling plots. 4 Linear Algebra and Least Squares: Solving systems of linear equations numerically and symbolically. Least squares regression and curve fitting. 4 Root Finding: Linearization and solving non-linear systems of equations. The Newton-Rapson method. 2 Computer Representation of Numbers: Integers and rational numbers in different bases. Floating point numbers. Round off and errors in basic arithmetic. Significant digits when reporting results. 4 Ordinary Differential Equations: Numerical integration and solving 1st order, ordinary differential equations (Euler’s method, Heun’s method and Runge-Kutta). Use of ODE function in MATLAB 4 System of Ordinary Differential Equations: Converting 2nd order and higher ODEs to systems of 1st order ODEs. Solving systems of ODEs via Euler’s method, Heun’s method and Runge-Kutta) 2 Non-Linear Differential Equations: Solving single and systems of non-linear differential equations by linearization. Use of the function ODE in MATLAB to solve differential equations. 2 Partial Differential Equations: The one-dimensional heat equation. Fourier series solution.

Student Survey Questions:

In this course I acquired the following:

1.       A knowledge of MATLAB usage for simulations

2.       An understanding of how systems are modeled and simulated

3.       The textbook was a useful reference and appropriate for the course.

4.       The final project was interesting, challenging, and appropriate for the course.