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2 cards from this section. Quick, good the night before a test.
What is a partial derivative?
Think of it as measuring change in one direction.
Write down the notation for the first-order partial derivative of u with respect to x.
Focus on the variable that is being differentiated.
What is the primary focus of a partial differential equation?
Remember, multiple independent variables are key.
True or False: Laplace's Equation is a type of linear PDE.
Focus on the structure and terms of the equation.
Prove that if u(x,y) is a solution of Laplace’s Equation in a region, then the average value of u over any circle in that region is equal to the value of u at the center of the circle.
Consider the implications of averaging values.
Analyze the behavior of a given boundary value problem for Laplace’s Equation in a rectangular domain: Given u(x,0) = f(x) and u(0,y) = g(y), find a method to determine solutions.
Focus on breaking the problem into solvable parts.
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