Gradient, Directional Derivative, and Potential Functions
Curriculum and historical examination lineage for Gradient, Directional Derivative, and Potential Functions under Unit 2 (Vector Calculus) of Advanced Calculus and Complex Analysis (21MAB102T) at SRMIST.
Historical appearance distribution across SRMIST Formative Tests (CT1, CT2) and University End Semester examinations.
Factual marks weightage of questions asked on this topic in historical examinations.
Question templates that recur across multiple examination cycles with similar conceptual stems.
“\text{Curl}(\text{grad } \phi) \text{ is} (A) \phi (B) 1 (C) -1 (D) 0”
“a. Find \(a, b, c\) so that the vector \(\vec{F} = (x+2y+az)\vec{i} + (bx-3y-z)\vec{j} +...”
“The unit vector normal to the surface \(x^2 + y^2 - z^2 = 1\) at \((1,1,1)\) is (A) \((\vec{i} +...”
“The unit normal vector to the surface \(x^2 + y^2 - z^2 = 1\) at \((1,1,1)\) is”
“The maximum directional derivative of \phi = xyz^2 at (1,0,3) is (A) 9 (B) 9\vec{j} + 6\vec{k} (C)...”
Representative historical questions extracted directly from SRMIST examination papers.
b. Show that \(\vec{F} = (2xy + z^3)\vec{i} - x^2\vec{j} + 3xz^2\vec{k}\) is a conservative vector field. Find the scalar potential also.
The unit normal vector to the surface \(x^2 + y^2 - z^2 = 1\) at \((1,1,1)\) is
The maximum directional derivative of \phi = xyz^2 at (1,0,3) is (A) 9 (B) 9\vec{j} + 6\vec{k} (C) 2\vec{i} + 4\vec{j} - \vec{k} (D) -9
Curl (grad \phi) (A) -1 (B) 1 (C) 0 (D) 2
The unit normal vector to the surface \(x^2 + y^2 - z^2 = 1\) at \((1, 1, 1)\) is (A) \((\vec{i} + \vec{j} - \vec{k}) / \sqrt{3}\) (B) \((2\vec{i} + 2\vec{j} - 2\vec{k}) /...
Examinations where questions for Gradient, Directional Derivative, and Potential Functions have appeared.
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