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Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define what a Partial Differential Equation (PDE) is.
π‘ Hint: Think about derivatives with multiple variables.
Question 2
Easy
What is the first step in eliminating arbitrary constants?
π‘ Hint: Think about using the definition of derivatives.
Practice 4 more questions and get performance evaluation
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What symbol is often used to denote βz/βx
?
π‘ Hint: Think about how we label derivatives in the examples.
Question 2
True or False: Arbitrary functions cannot be eliminated when forming PDEs.
π‘ Hint: Consider the methods we discussed for handling functions.
Solve 1 more question and get performance evaluation
Push your limits with challenges.
Question 1
Given the function z = e^(ax + by) + c
, derive the PDE by eliminating c
.
π‘ Hint: Focus on how the exponential responds to differentiation.
Question 2
Take the function z = x^2 + y^2 + f(x-y)
; eliminate f
to derive the PDE.
π‘ Hint: Pay attention to how the difference in `x` and `y` is expressed in terms of `f`.
Challenge and get performance evaluation