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MATH 4990

Mathematical Models and Their Analysis

Read Sections 3.1.1, 3.1.2 (up to Eq. (3.10)) and 3.1.3 of Lecture 3. You may also read both Appendices; they are FYI and will not be needed to do HW.
Attempt Problems 1(a) and 2(a) of HW 3

Background from Algebra, Precalculus, Calculus and Linear Algebra whose knowledge I will assume (and therefore will not review) in this course.
If you need to review any of this background material, you may find it, for example, at Paul's Online Notes or OpenStax.

Policy on allowed and non-allowed collaboration on homework assignments
Your assignments must be prepared neatly and be stapled together. I will not accept sloppily written work or unstapled sheets.
For graduate students only: Bonus (extra credit) problems, which are optional for undergraduate students, are required for graduate students.
You are not required to type your homework. However, if you decide to type it, and do so in Latex, here is a list of Latex commands for typesetting mathematical symbols. Again, this is not a concealed request to type your homework; I'll accept handwritten work as long as it is neat and legible.

While some of the homework problems will require the use of symbolic calculations, most of them (if not all) can be done online via publicly available Wolfram Alpha.
Another way to avoid installing Mathematica is to log into its Cloud version: https://www.wolframcloud.com/. Sign in using your UVM email (use the option Sign in with Single Sign-on (SSO)) and then, at a prompt, UVM password and then open a new Notebook.
If you prefer to download a copy of Mathematica, go to the UVM Software Portal, find Mathematica, and follow your nose to install it (you will need to enter your UVM netID and password). Between the two download options, you can choose Manager vs Full Installer, as the former is a bit faster. After installing, the system will ask you to activate Mathematica if you don’t already have an active license on your computer. Choose Activate Through Your Organization (SSO), enter your UVM email and follow your nose.
There is a new feature in Mathematica 14, called "Free-form output," available both in an installed copy of the program and in WolframCloud (but not in Wolfram Alpha). To see how it works, at the input begin typing something like "solve cos x + sin x = 0.5" or "find root of x^2-1" (without quotes). A drop-down menu will appear, one of whose options is "Convert to free-form output." Select it and see what happens.

This manual is 30+ years old, yet it is one of the best written getting-started manuals that I know of. You need to read only up to the end of p. 9 plus section 18 (graphics).
Introduction to Matlab by R.L. Spencer and M.J. Ware of Brigham Young University
- Here is the pdf file if the above link does not work.

MATLAB Primer by S. Nakamura. This is Chapter 1 from the book "Numerical Analysis and Graphic Visualization with MATLAB," 2nd ed.

Guidelines for your midterm and final presentations <-- Read those early on, before even starting to prepare for the midterm presentations

A paper related to Linear Algebra; will be determined and posted by February 17.

Background information from Linear Algebra
Notes on Gram-Schmidt orthogonalization and QR factorization from "Linear Algebra with Applications", 9th Ed., by S.J. Leon
Notes on SVD from "Linear Algebra: A Modern Introduction", 4th Ed., by D. Poole:

my own notes on SVD
Notes on Information Retrieval from "Linear Algebra with Applications", 8th Ed., by S.J. Leon:

Additional (optional) materials that may be related to the midterm project: