8/16/2019 Iit Mathematics Test Jam 2015 Syllabus
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SYLLABUS FOR M.SC. (MATHS) AS PER JAM 2015 ( FOR IITs):
MATHEMATICS (MA)
Sequenes !n" Se#$es %& Re!' u*e#s: Sequences and series of
real
numbers, Convergent and divergent sequences, bounded and
monotone
sequences, Convergence criteria for sequences of real numbers,
Cauchy
sequences, absolute and conditional convergence; Tests of
convergence for
series of positive terms – comparison test, ratio test, root
test; Leibnitz test
for convergence of alternating series
Fun+$%ns %& One ,!#$!*'e: limit, continuity,
di!erentiation, "olle#s
Theorem, $ean value theorem Taylor%s theorem $a&ima
and minima
Fun+$%ns %& T-% Re!' ,!#$!*'es: limit, continuity, partial
derivatives,di!erentiability, ma&ima and minima $ethod of
Lagrange multipliers,
'omogeneous functions including (uler#s theorem
In+e#!' C!'u'us: )ntegration as the inverse process of
di!erentiation,
de*nite integrals and their properties, +undamental theorem of
integral
calculus ouble and triple integrals, change of order of
integration
Calculating surface areas and volumes using double integrals
and
applications Calculating volumes using triple integrals and
applications
/$e#en+$!' Equ!+$%ns: -rdinary di!erential equations of the *rst
order of the form y%.f/&,y0 1ernoulli#s equation,
e&act di!erential equations,
integrating factor, -rthogonal tra2ectories, 'omogeneous
di!erential
equations3separable solutions, Linear di!erential equations of
second and
higher order 4ith constant coe5cients, method of variation of
parameters
Cauchy3(uler equation
,e+%# C!'u'us: Scalar and vector *elds, gradient, divergence,
curl and
Laplacian Scalar line integrals 67 and vector line integrals,
scalar surface
integrals and vector surface integrals, 8reen%s, Sto9es and
8auss theorems
and their applications
#%u T3e%#4: 8roups, subgroups, belian groups, non3abelian
groups,
cyclic groups, permutation groups; ormal subgroups, Lagrange%s
Theorem
for *nite groups, group homomorphisms and basic concepts of
quotient
groups /only group theory0
