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3 cards from this section. Quick, good the night before a test.
Define an algebraic equation.
Think of equations with x raised to whole number powers.
What is the primary condition for the Bisection Method to work?
Remember the sign change condition.
What kind of equations can be solved using numerical methods?
Consider examples discussed in class.
The Bisection Method can only be applied if:
Think about the conditions for continuity.
Use the Newton-Raphson method to find the root of the equation f(x) = x^2 - 3 starting from an initial guess x₀ = 2. Show the calculations for three iterations.
Calculate f(x) and its derivative at each iteration.
Explain how you would use the Fixed Point Iteration to solve for x in the equation x = 2x - 1. Iterates from x₀ = 1 until convergence.
Keep track of how the value changes each iteration.
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