Gauhati University Question Papers for Mathematics 4th Semester
Gauhati University Question Papers for Mathematics 4th Semester
Question Paper from 2010 available
More than 50 question papers every semester
Please check your syllabus before downloading the question paper.
If syllabus does not match then don't download the question paper.
Year
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Paper 101
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Paper 102
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2010
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More than 50 question papers every semester
4th Semester Revised Syllabus of Mathematics For Three
year Degree Course ( Major Course)
Real Analysis
Unit1: Characterization of the real number system
R as a complete Archimedean ordered field, neighbourhoods, open set, closed
set, limit point of a set Bolzano-Weierestress theorem for a set, nested
interval theorem.
Sequence of real numbers, bounded and unbounded sequences,
subsequences, limit of a sequence, Bolzano-Weierestress theorem for
bounded sequences, limit superior and limit inferior, convergent and divergent sequence,
Cauchy sequences, Cauchy’s principle of convergence, convergence and divergence
of monotonic sequences, algebraic operation on limits, sandwich theorem,
Cauchy theorem on limit.
Unit 2:Infinite series, convergence ,divergence and
Cauchy’s general principle of convergence, introduction and removal of
brackets, multiplication of series and double series, comparison test, Cauchy’s
root test, D’Alembert’s ratio test( with proof),statement ( without
proof) of Raabe’s test, logarithmic test, Gauss test, Cauchy’s
condensation test, Cauchy’s integral test for testing the convergence of
series of positive terms, Abel’s theorem, alternating series and Leibnitz’s test,
absolute and conditional convergence, statement and application of Riemann
theorem and Dirichlet’s theorem( without proof)
on the rearrangement of terms of an infinite
series.
Unit 3: ( ,δ) definition of limit and
continuity of a function of single variable, properties of continuous
functions in closed interval, sequential continuity, inverse function and
monotonic function, uniform continuity.
Unit 4: Derivability of a function of
single variable, algebra of derivatives, Darboux’s theorem, intermediate value
theorem for derivatives, Roll’s theorem, mean value theorems,
intermediate forms, Taylor’s theorem, Taylor’s and Maclaurin’s infinite
series, expansion of e x , sin x, cos x, log(1 + x)and (1 + x) m ,maxima-minima
of a function of single
variable and two variables (reducible to single variable).
Mechanics
Unit 1: Parallel forces, couples, reduction
of coplanar forces, analytical condition of equilibrium of coplanar
forces, friction.
Unit2: Centre of gravity of a plane area,
arc and a sector of a curve, C.G of solids and surface of revolution, C.G
of areas bounded by a given curve.
Unit3: Principle of virtual work-in two dimensions,
forces in three dimensions.Poinsot’s central axis, wrenches, null lines
and planes.
Unit 4: Stable and unstable equilibrium.
Unit5: Velocities and acceleration along radial and
transverse directions and along tangential and normal
directions, motion in a straight line under variable acceleration, simple
harmonic motion and elastic string.
Unit6: Motion on smooth and rough plane curves, motion
in resisting medium, motion of particles of varying mass.
Unit7: Central orbit and Kepler’s laws of
planetary motion.
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