Taylor's and Laurent's Series Expansions
Curriculum and historical examination lineage for Taylor's and Laurent's Series Expansions 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.
“If f(z) is analytic inside and on C, the value of \oint_{C} \frac{f(z)}{z-a}dz, where 'C' is a...”
“Expand \(f(z) = \frac{z^2 - 1}{(z+2)(z+3)}\) in a Laurent's series if \((i) |z| < 2, (ii) |z| > 3,...”
“a. If \(f(z) = \frac{1}{(z-1)(z-2)}\) expand as Laurent's series about \(z=0\) valid in \((i) |z| <...”
“Answer the following subquestions. (i) Using Cauchy integral formula evaluate \(\int_c...”
“The part \sum_{n=0}^{\infty} a_n(z - a)^n consisting of positive integral powers of (z - a) is...”
Representative historical questions extracted directly from SRMIST examination papers.
a. If \(f(z) = \frac{1}{(z-1)(z-2)}\) expand as Laurent's series about \(z=0\) valid in \((i) |z| < 1 \quad (ii) 1 < |z| < 2\) --- OR --- 25.b. Evaluate \(\oint_c \frac{\sin \pi...
Expand \(f(z) = \frac{z^2 - 1}{(z+2)(z+3)}\) in a Laurent's series if \((i) |z| < 2, (ii) |z| > 3, (iii) 2 < |z| < 3\). (b) Expand \(f(z) = \frac{z^2 - 1}{(z+2)(z+3)}\) in a...
Evaluate \int_C \frac{(z-1)dz}{z^2(z+1)^2(z-2)} where C is |z-i|=2. (a) Evaluate \int_C \frac{(z-1)dz}{z^2(z+1)^2(z-2)} where C is |z-i|=2. --- OR --- 25. Expand f(z) =...
Expand f(z) = \frac{1}{z^3-3z+2} in a Laurent's series in the region (i) 1 < |z| < 2 (ii) 0 < |z-1| < 2. (b) Expand f(z) = \frac{1}{z^3-3z+2} in a Laurent's series in the region...
Expand \(f(z) = \frac{z^2 - 1}{(z + 2)(z + 3)}\) in a Laurent's series if \((i) \quad |z| < 2 \quad (ii) \quad |z| > 3 \quad (iii) \quad 2 < |z| < 3\)
Examinations where questions for Taylor's and Laurent's Series Expansions have appeared.
Master Taylor's and Laurent's Series Expansions in MintAI
Practice past exam questions, test recurring archetypes, and view predictive probability for this topic before your upcoming exam.