University:
Whitman College
Course:
MATH-225 | Calculus III
Academic year:

2023
Views:

201

Pages:

1
Author:

bendypennisetum

Supplementary Exercises for Sections 13.6 1. How many third-order derivatives does a function of 2 variables have? How many of these are distinct? 2. How many nth order derivatives does a function of 2 variables have? How many of these are distinct? 3. Let α and k be constants. Prove that the function u(x, t) = e−α 2 k2 t sin(kx) is a solution to the heat equation ut = α2 uxx 4. Let a be a constant. Prove that u = sin(x − at) + ln(x + at) is a solution to the wave equation utt = a2 uxx . 5. Let f (x, y) be a continuous differentiable function. Analyze the level curves near a critical value if that critical value is a max or a min. What if the level curve is a saddle point? 1

Calculus Supplementary Exercises

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