Solution of an Equation by using MATLAB

Mahmud Akelbek
Weber State university,
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Summary

This module can be used in Introduction to Numerical analysis courses as a supplemental material. In a senior undergraduate math topic course, it can be also used as a short introduction to solving equations of one variable by using MATLAB.

We will consider one of the basic problems in numerical approximation, the root-finding problem. We will introduce five different ways to approximating the solutions of a root finding problem: the Bisection method, the Newton's method, the Fixed-point method, the Secant method, and the False Position method. Students will also construct computer code and test their results for different problems.

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Learning Goals

Learn different methods of solving equations of one variable

Compare and contrast advantages and disadvantages of different algorithms

Compare the rates of convergence for different algorithms

Construct MATLAB code for different algorithms and test the results

Context for Use

This module can be used for students who have taken calculus II. Students also need to have beginning level of MATLAB programming. It can be used as two-hour classroom instruction and two-hour lab time for computer programming.

Description and Teaching Materials


The MATLAB code for the Newton's method (Acrobat (PDF) 46kB Sep29 16)
The MATLAB code for the Bisection method (Acrobat (PDF) 41kB Sep29 16)
The MATLAB code for the Secant method (Acrobat (PDF) 29kB Sep29 16)
The MATLAB code for the False Position method (Acrobat (PDF) 44kB Sep29 16)
The MATLAB code the Fixed Point method (Acrobat (PDF) 48kB Sep29 16)

Teaching Notes and Tips

Assessment

Students will be assigned a list of problems that will require them to solve by using computer programming.

References and Resources

Numerical Analysis, Richard L. Burden, J. Douglas Faires, 9th edition



Numerical Analysis, Richard L. Burden, J. Douglas Faires, book companion site

https://sites.google.com/site/numericalanalysis1burden/home