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2 cards from this section. Quick, good the night before a test.
Compute the exact value of C6(1, 1) for C6(x, y) = e^(x+y).
Use direct substitution into the function.
What is B4C6/B4x for C6(x, y) = e^(x+y)?
Differentiate with respect to x.
What is the exact value of B4C6/B4x at (1, 1)?
Think about what happens when you differentiate.
Is the PDE elliptic when M < 1?
Recall the classifications discussed.
Given the function C6(x, y) = e^(x+y), calculate and interpret the exact and approximate values of B4C6/B4x at (1, 1) and discuss the implications if M is varied.
Explore numerical methods comparisons in fluid dynamics.
Determine the role of percentage difference in finite differences and its relation to the accuracy of M-based classifications in PDEs.
Think critically about how error affects theoretical and applied fluid dynamics.
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