2.086 | Fall 2014 | Undergraduate

Numerical Computation for Mechanical Engineers

Nutshells & GUIs

Unit I: (Numerical) Calculus—Interpolation, Integration, Differentiation

Interpolation (PDF)

Integration (PDF)

Differentiation (PDF)

Unit I GUIs (ZIP) (This ZIP file contains: 3 .fig files and 3 .p files.)

Note: To run the interpolation gui, type 
interpolation_gui(from within the \guis" folder) in the MATLAB® command window; similarly for the integration_gui and differentiation_gui.

Unit II: Probability; Statistical Estimation; Monte-Carlo Methods

Introduction to Probability and Statistics: A Frequentist Perspective (PDF - 2.9MB)

Random Variables (PDF)

Monte Carlo Integration (PDF)

Unit II GUIs (ZIP) (This ZIP file contains: 2 .fig files and 2 .p files.)
Unit III: (Numerical) Linear Algebra I—Matrices and Vectors, Least-Squares; Regression

Fitting a Model to Data: Least Squares Formulation (PDF)

Matrices and Vectors (PDF)

Regression: Least Squares and Statistical Inference (PDF)

Unit III GUIs (ZIP) (This ZIP file contains: 2 .fig files and 2 .p files.)

Note: To launch a GUI_NAME_gui.p", you should enter NAME_gui in the MATLAB command window. In general, it will not work to double-click on the file name.

Unit IV: Numerical Ordinary Differential Equations (ODEs); Eigenproblems

Numerical Treatment of Initial Value Problem (IVP) Ordinary Differential Equations (ODEs) (PDF)

Stability: ODEs and Eigenproblems (Video) 
(The first few minutes of the video address a topic beyond our 2.086 coverage, but the remainder of the video is germane to 2.086 and, in particular, directly relevant to Question 6 of Assignment 4.)

There are no GUIs for this unit.
Unit V: (Numerical) Linear Algebra II—Linear Systems; Nonlinear Systems

Linear Systems of Equations (PDF)

In addition, the following material from the textbook should prove useful for Assignment 5: Chapters 24, 26, and 27. (Electively, you may read Chapter 29 of the textbook for some background on nonlinear problems, however this chapter is not required for Assignment 5: Assignment 5 includes a self-contained discussion of nonlinear problems (and associated MATLAB issues).)

Unit V GUIs (ZIP) (This ZIP file contains: 1 .fig file, 1 .mat file, and 1 .p file.)

Note: This GUI provides a visualization of the LU procedure and associated fill-in with special attention to sparse matrices. The associated material may be found in Chapters 26 and 27 of the textbook.

Course Info

Learning Resource Types
Online Textbook
Demonstration Videos
Programming Assignments