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MANE 3351 - Manufacturing Engineering Analysis

Laboratory 8 Assignment

Assigned: October 28, 2024

Due: November 4, 2024 (before 3:30 pm)

Learning Goals

  1. Utilize graphical analysis to determine starting points for bracketed and non-bracketed root finding methods, and
  2. Implement a bracketed and non-bracketed root finding method.

Description

Conside the function shown below on the interval of [0.5,1.0].

\[ f(x)=4x^3-3x=0 \]

Step 1

Edit the first cell (markdown), to update your personal information for laboratory 8.

Step 2

In cell two, complete the following steps:

  • Create a user-defined function for equation provided in the description,
  • Vectorize the user-defined function,
  • Create an array for the x-values on the interval of [0.5, 1.0] that contains at least 100 points,
  • Create an array for the y-values using the vectorized function that contains the values of the vectorized x-values,
  • Use Matplotlib to create an x-y graph, and
  • Identify a pair of starting values that brackets the root.

Step 3

In cell three, implement one of the bracketed root finding methods using the start values found in step two to find the root with a tolerance of 10^-5. Your code in cell three should print the value of the root and the error.

Step 4

In cell four, implement one of the non-bracketed root find methods for the function described in the description. Use one of the bracketing values identified in step as the starting value. Find the root with a tolerance of 10^-5. Your code in cell three should print the value of the root and the error.

Step 5

After running and testing your program, save the Jupyter Notebook. Upload your repository using GitHub desktop.