# Computational Methods

Autar Kaw

Univesity of South Florida

#### Summary

Develop and use numerical methods for the following mathematical procedures and topics - Differentiation, Nonlinear Equations, Simultaneous Linear Equations, Interpolation, Regression, Integration, and Ordinary Differential Equations.

Calculate errors and their relationship to the accuracy of the numerical solutions is emphasized throughout the course.

Program via MATLAB to reinforce the fundamentals of the course as well as to solve intractable/real-life problems.)

Course URL: http://www.eng.usf.edu/~kaw/class/EML3041/
Course Size:

31-70

Course Format:

Lecture only

Institution Type:

University with graduate programs, including doctoral programs

## Course Context:

It is a required junior-level course for students in Mechanical Engineering major. It follows the Calculus sequence and Ordinary Differential Equations. The programming course is also a prerequisite to the course.

## Course Content:

Develop and use numerical methods for the following mathematical procedures and topics - Differentiation, Nonlinear Equations, Simultaneous Linear Equations, Interpolation, Regression, Integration, and Ordinary Differential Equations.

Calculating errors and their relationship to the accuracy of the numerical solutions are emphasized throughout the course.

Program via MATLAB to reinforce the course's fundamentals and solve intractable/real-life problems.

## Course Goals:

Develop mathematical models for solving complex engineering problems;

Reinforce programming skills using the MATLAB environment to solve intractable/real-life problems;

Calculate, quantify, and minimize errors in solving complex engineering problems where neat analytical solutions may not exist;

Solve the following types of problems numerically when needed in other courses and real-world applications:

Computation of derivatives and integrals

Nonlinear equations

Systems of simultaneous equations

Curve fitting (interpolation and regression) of discrete data

Integration of continuous and discrete functions

Ordinary differential equations (initial value or boundary value problems)

## Course Features:

One computer project is broken into two mini-projects with two separate deadlines. The project is broken into two mini ones for two reasons – to reduce the end-of-semester rush of completing a large project, but more importantly, to receive feedback on the first mini project and use that to improve your submission of the second one.

## Assessment:

Students are assigned online adaptive lessons (graded), which need to be completed before coming to class. After going through this lesson, be sure to finish the chapter by

1) coming to class to listen to short lectures and participate in individual and group activities such as clicker questions (ungraded) and free-response questions (ungraded),

2) reading the assigned textbook pages,

3) solving and/or peeking into the solution of the assigned multiple-choice question set (ungraded), and

4) solving the assigned problem set questions from the textbook on this chapter (ungraded).

There are six tests – three unit tests (42% of course grade), a programming prerequisite test (3%), Fundamentals of Numerical Methods test (5%), and one final examination (25% of course grade). Tests are all held during scheduled class time, and the final will be during the time slot of the final examination week.

## Syllabus:

[file Sylllabus for EML3041 Computational Methods (Acrobat (PDF) 12.9MB Aug18 22) 'Syllabus']

## References and Notes:

Numerical Methods with Application by Autar Kaw, et al
It is an open educational resource written by the instructor. It meets the needs of my students in a concise fashion without the bloat.

I have been teaching it using flipped/adaptive pedagogy.  The following books have assisted me in my pedagogy

A mind for numbers ; Understanding by Design; How Learning Works: Seven Research-Based Principles for Smart Teaching; Creating significant learning experiences; Make it Stick