MANE 3351
Lecture 9, September 20
Classroom Management
Agenda
- Example problem from Wednesday
- Lecture
- Lab today!
Resources
Handouts
Calendar
| Lecture | Date | Content |
|---|---|---|
| 1 | August 23 | Welcome to Class, Syllabus |
| 2 | August 25 | Error Analysis |
| 3 | August 30 | Introduction to Jupyter Notebook |
| 4 | September 1 | Markdown |
| 5 | September 6 | Labor Day Holiday |
| 6 | September 8 | Taylor Polynomials, Homework 1 |
| 7 | September 13 | Roots of Equations, Bisection Method |
| 8 | September 15 | Bisection Error Analysis |
| 9 | September 20 | False Position Algorithm |
Assignments
- Homework 2 (assigned 9/15/2021, due 9/23/2021)
False Position
- Attempts to converge faster than bisection method by using functional information
- Referred to as the secant method in textbook
- The new root is found by
\[
x_r=x_u-\frac{f(x_u)(x_l-x_u)}{f(x_l)-f(x_u)}
\]
- Figure 5.12 (Chapra and Canale(2015)[^1] illustrates the false position method
False Position Code
The pseudocode, shown below was taken from [^2]
Jupyter Notebook Demonstration
False Position Error Analysis
- Much harder to analyze than bisection method
- Convergence to root depends on shape of \(f(x)\)
- At times, false position may converge slowly!, Example from textbook[^3], shown below
Loops in Python
- Python only supports two types of loops: for and while
- Pseudocode used do/while loop
[1]: Chapra, S. and Canale, R. (2015), Numerical Methods for Engineering, 7th edition
[2]: Source: https://www.codesansar.com/numerical-methods/regula-falsi-or-false-position-method-pseudocode.htm
[3]: Brin, L., (2020), Tea Time Numerical Analysis: Experiences in Mathematics, 3rd edition