Practice Final Tip - 1.4 | 1. Formation of Partial Differential Equations | Mathematics - iii (Differential Calculus) - Vol 2
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Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define what a Partial Differential Equation (PDE) is.

πŸ’‘ Hint: Think about derivatives with multiple variables.

Question 2

Easy

What is the first step in eliminating arbitrary constants?

πŸ’‘ Hint: Think about using the definition of derivatives.

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Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What symbol is often used to denote βˆ‚z/βˆ‚x?

  • p
  • q
  • r

πŸ’‘ Hint: Think about how we label derivatives in the examples.

Question 2

True or False: Arbitrary functions cannot be eliminated when forming PDEs.

  • True
  • False

πŸ’‘ Hint: Consider the methods we discussed for handling functions.

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Challenge Problems

Push your limits with challenges.

Question 1

Given the function z = e^(ax + by) + c, derive the PDE by eliminating c.

πŸ’‘ 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.

πŸ’‘ Hint: Pay attention to how the difference in `x` and `y` is expressed in terms of `f`.

Challenge and get performance evaluation