21.19 - Vector Calculus Foundations (Bridge Topic)
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Practice Questions
Test your understanding with targeted questions
Define the gradient in your own words.
💡 Hint: Think about how it maps a scalar to a direction.
What does divergence measure?
💡 Hint: Think of how fluids enter or leave a region.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the gradient of a scalar field indicate?
💡 Hint: Consider where you'd look to find the quickest path uphill.
Is the curl of a vector field always zero?
💡 Hint: Think about when you see spiraling motion.
1 more question available
Challenge Problems
Push your limits with advanced challenges
A scalar field is defined as T(x,y) = 3x^2 + 2y^2. Calculate the gradient of T at the point (2, 1).
💡 Hint: Differentiate with respect to x and y to find the gradient vector.
Given a vector field V(x, y, z) = (xz, y^2, xy), calculate its divergence.
💡 Hint: Apply the divergence operator using partial derivatives across each component.
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