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.

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