1.1 - Introduction to Numerical Methods
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Practice Questions
Test your understanding with targeted questions
Define absolute error in your own words.
💡 Hint: Think about what it means to be exact.
How is relative error calculated?
💡 Hint: Use the formula: Relative Error = |x_exact - x_approx| / |x_exact|.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is absolute error?
💡 Hint: Remember the definition you learned in class.
Is the following statement true or false? 'Stability in numerical algorithms means that errors will not grow during calculations.'
💡 Hint: Think about what stability means in an everyday context.
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Challenge Problems
Push your limits with advanced challenges
Given the equation x = 1/(1-x), analyze how small changes in x affect the output when x approaches 1. Discuss whether the function is well or ill-conditioned.
💡 Hint: Use the concept of derivatives to help understand the sensitivity.
Describe a scenario in engineering where numerical stability is critical. What can happen if an unstable algorithm is used?
💡 Hint: Consider systems where safety is a priority.
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