Green's Theorem in a Plane
Curriculum and historical examination lineage for Green's Theorem in a Plane 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.
“If \(\vec{r}\) is the position vector of the point \((x,y,z)\) with respect to the origin then...”
“Verify Green's theorem in a plane for \iint_{R} (3x^{2}-8y^{2})dx+(4y-6xy)dy where 'c' is the...”
“Using Green's theorem, evaluate \int_C (x^2 - y^2) dx + 2xy dy where C is the closed curve of the...”
“Vector differentiation and Green's theorem. (a) i. Find the directional derivative of the function...”
“Show that \vec{F} = (2x + yz)\vec{i} + (4y + zx)\vec{j} - (6z - xy)\vec{k} is irrotational and...”
Representative historical questions extracted directly from SRMIST examination papers.
Vector differentiation and Green's theorem. (a) i. Find the directional derivative of the function \phi = 2yz + z^2 in the direction of the vector \vec{i} + 2\vec{j} + 2\vec{k} at...
Verify Green's theorem in a plane for \iint_C [(3x^2 - 8y^2)dx + (4y - 6xy)dy] where C is the boundary of the region defined by the lines x=0, y=0 and x+y=1. (b) Verify Green's...
Verify Gauss-Divergence theorem for \vec{F}=x^{2}\hat{i}+z\hat{j}+y\hat{z} over a cube formed by 0 \le x \le 1, 0 \le y \le 1, 0 \le z \le 1. --- OR --- 29. Verify Green's theorem...
Verify Green's theorem in a plane for \iint_{R} (3x^{2}-8y^{2})dx+(4y-6xy)dy where 'c' is the boundary of the region defined by x=y^{2} and y=x^{2}.
Prove that \vec{F} = (y^2 \cos x + z^3)\vec{i} + (2y \sin x - 4)\vec{j} + 3xz^2\vec{k} is irrotational and find its scalar potential. (a) Prove that \vec{F} = (y^2 \cos x +...
Examinations where questions for Green's Theorem in a Plane have appeared.
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