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Teacherbot 30 Mar, 03:52:41

Exercise Title: Numerical Analysis using Python: Root Finding and Optimization

Objective: To introduce students to the concepts of root finding and optimization in numerical analysis using Python.

Materials Needed: - Computer lab with Python installed - Jupyter Notebook or any Python IDE - Sample datasets for root finding and optimization

Exercise Steps:

  1. Introduction to Root Finding - Explain the concept of root finding and its importance in numerical analysis. - Discuss the different methods of root finding such as bisection, Newton-Raphson, and secant method. - Provide sample datasets for root finding.

  2. Root Finding Exercise - Instruct students to open a Jupyter Notebook or any Python IDE. - Provide a sample dataset for root finding. - Ask students to implement the bisection method to find the root of the given dataset. - Instruct students to compare the results with the Newton-Raphson and secant method.

  3. Introduction to Optimization - Explain the concept of optimization and its importance in numerical analysis. - Discuss the different methods of optimization such as gradient descent, Newton’s method, and conjugate gradient method. - Provide sample datasets for optimization.

  4. Optimization Exercise - Instruct students to open a Jupyter Notebook or any Python IDE. - Provide a sample dataset for optimization. - Ask students to implement the gradient descent method to optimize the given dataset. - Instruct students to compare the results with the Newton’s method and conjugate gradient method.

  5. Conclusion - Recap the concepts of root finding and optimization. - Discuss the importance of these concepts in real-world applications. - Encourage students to explore more advanced topics in numerical analysis using Python.

Assessment: - Students’ ability to implement the bisection, Newton-Raphson, and secant method for root finding. - Students’ ability to implement the gradient descent, Newton’s method, and conjugate gradient method for optimization. - Students’ ability to compare and analyze the results of different methods.