Math 2650 - Intro to Computational Math - Fall 2015
Dr. Radu C. Cascaval

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Required Materials:

Textbook: MATLAB: An Introduction with Application, by Amos Gilat, 5th edition, 2014, ISBN 978-1-118-62986-4 (see it on amazon.com)

MATLAB is available to all UCCS students in most IT computer labs on campus (including library).
Starting with Spring 2016, it is available for free to all UCCS students.

Course Description:

Computing is an essential part of modern mathematics. Many scientific endeavors require knowledge of sophisticated mathematical tools, which are computational in nature. This one-credit hour course is a hands-on introduction to computations as a problem solving tool in mathematics, using primarily the MATLAB platform. The labs will cover arrays and mathematical operations with arrays, representation of mathematical equations and functions using arrays, visualization of data and functions. MATLAB programming, including general program organization, m-files, built-in mathematical functions as well as user-defined functions, and symbolic math computations will be thoroughly discussed. Applications such as solving equations in one and several variables, finding min/max of a function, numerical integration will be highlighted. A more detailed list of topics is included in the course outline below.

Computational Objectives:

The main goal of this course is to learn how to solve mathematical problems that require computational power. MATLAB will be the prefered platform for pursuing this goal. No prior experience with MATLAB is required. The labs are designed to introduce the student to MATLAB and how it can be used in solving mathematical problems. At the end of this course the student should be able to:

- decide when and how much to rely on a computer in the process of solving a mathematical problem
- develop the necessary code, test the code and analyze the outcome of the code
- use the computer output to present the solution to the original problem and gain further insight in the problem and its solution.

Targeted audience:

Students majoring in math, science and engineering who want to get a head start in learning computational tools and their use in handling mathematical concepts. In particular this course is well suited for students who plan to enroll in courses where MATLAB is a companion software, such as Linear Algebra, Differential Equations, Numerical Analysis, Mathematical Modeling, Stochastic Modeling, Optimization and more. Prerequisite course: Math 2350.

Supplementary Resources:

1. Essential Matlab for Engineers and Scientists, by Brian Hahn Dan Valentine, 4th Edition, Oct 2009
(FREE* chapter-by-chapter download for UCCS students)
[*You must be on the campus network to be able to freely download individual chapters of the book].

2. Numerical Computing with MATLAB, by Cleve Moler, SIAM 2008 (revised edition)
(freely downloadable at http://www.mathworks.com/moler/. You may also purchase a paperback copy from SIAM website.

3. Experimenting with MATLAB, by Cleve Moler, Electronic book (freely downloadable at http://www.mathworks.com/moler/.)

4. An Introduction to Programming and Numerical Methods in MATLAB, by S.T. Otto and J.P. Denier, Springer 2005
(FREE* download for UCCS students on Springerlink.com)

5. MATLAB: A Practical Introduction to Programming and Problem Solving, by Stormy Attaway, Elsevier 2009

Topics Covered:

1. Starting with MATLAB. Script Files |
2. Creating Arrays. Mathematical Operations with Arrays |
3. Symbolic vs Numeric World |
4. 2d Plots |
5. Programming in MATLAB |
6. User-Defined Functions and Function Files. Data Management |
7. Polynomials. Interpolation and Curve Fitting. |
8. 3D Plotting |
9. Applications to Numerical Analysis |
10. Numerical Integration and Solving ODEs |