Practice Elementary Finite Difference Quotients (6.1) - Computational fluid dynamics (Contd.)

Practice: Elementary Finite Difference Quotients

Lesson 6.1Computational fluid dynamics (Contd.)

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9 questions

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6 sample questions

Question 1.
Define finite difference quotient.
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Think about how we use data points to estimate change.
Question 2.
What does truncation mean in the context of numerical methods?
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Consider what happens when you only keep part of a mathematical series.
3Question 3.
What is the purpose of finite difference quotients?
- To calculate area under curves
- To approximate derivatives
- To simplify algebraic equations
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Focus on the role they play in numerical methods.
4Question 4.
True or False: The forward difference uses the data point from behind the current point.
- True
- False
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Think about the data point directions.
Question 5.
Given a function f(x) = x^2, compute the forward and backward finite difference quotients at x=2 using a step size of 0.1.
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Use the finite difference formulations to substitute values.
Question 6.
Discuss how increasing the number of points in a Taylor series expansion affects truncation error and approximation accuracy.
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Think about how much information we lose with fewer terms.

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