Cauchy's Residue Theorem
Curriculum and historical examination lineage for Cauchy's Residue Theorem under Unit 5 (Complex Integration) 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.
“Answer the following subquestions. (i) Using Cauchy integral formula evaluate \(\int_c...”
“\text{The connection between a line integral and the double integral is known as} (A) \text{Stoke's...”
“By Cauchy's residue theorem, the value of \oint_{C} \frac{z}{z - 3} dz where C is the circle |z| =...”
“\int_0^{2\pi} \frac{d\theta}{5 + 4 \cos \theta} by calculus of residues. --- OR --- 32. Find the...”
Representative historical questions extracted directly from SRMIST examination papers.
Answer the following subquestions. (i) Using Cauchy integral formula evaluate \(\int_c \frac{z}{z-2} dz\), where \(c\) is the circle \(|z - 2| = \frac{3}{2}\). (ii) Evaluate...
Answer the following subquestions: (a) Using Cauchy integral formula evaluate \(\int_{c} \frac{z}{z - 2}dz\), where \(c\) is the circle \(|z - 2| = 3/2\). (ii) Evaluate \(\int_{c}...
The relation between line integral and a surface integral is known as (A) Green's theorem (B) Residue theorem (C) Stokes theorem (D) Divergence theorem
By Cauchy's residue theorem, the value of \oint_{C} \frac{z}{z - 3} dz where C is the circle |z| = 2 is
\int_0^{2\pi} \frac{d\theta}{5 + 4 \cos \theta} by calculus of residues. --- OR --- 32. Find the Laurent expansion to represent the function f(z) = \frac{z^2 - 1}{(z + 2)(z + 3)}...
Examinations where questions for Cauchy's Residue Theorem have appeared.
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