Header Ads

Breaking News
recent

Gauhati University Question Papers for Mathematics 5th Semester

Gauhati University Question Papers for Mathematics 5th 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
Paper 101
 Paper 102
2010
Download
Download
2011
Download
Download
2012
2013
2014
Download
Download
2015
2016
2017
Download
Download

This is the downloading page for Mathematics 5thsemester but if 

you want to explore the world of mathematics than go to the main 

page for Mathematics major. Find the all the help form the world 

of education so please comment. 



Link is below down here



Main page- link










The Syllabus for the Subject is not available so please comment if you need the syllabus urgently.





5th Semester
Revised Syllabus of Mathematics
For
Three year Degree Course ( Major Course) Paper-M501
Real and Complex Analysis

Unit1: Limit and continuity of a function of several variables, partial derivatives, differentiability, Young’s and Schwarz’s theorems, differentials of higher orders, differentiation of composite functions, change of variables , Taylor’s theorem for two variables, implicit functions, only statement of implicit theorem on two variables with its applications, jacobians, maxima and minima, LaGrange’s method of multiplier 
Unit2: Riemann integral, integrability conditions, Riemann integral as a limit, some classes of  integrable  functions , the fundamental theorem of integral calculus, statement and application of M.V. theorems of integral calculus.                                         
Unit3: Improper integrals and their convergence, various forms of comparison tests, absolute and conditional convergence, Abel’s and Dirichlet’s tests, beta and gamma functions, Frullani’s integral, integral as a function of parameter( excluding improper integrals), continuity, derivability and integrability of an integral as a function of a parameter.                                                                                                            
 Unit4: Theorems on limit and continuity of a function of complex variable, uniform continuity, differentiability of a function of complex variable, analytic functions, Cauchy- Riemann equations, harmonic functions, differentials, derivatives of elementary
functions, L’Hospital’s rule , stereographic projection.                                    
Unit5: Rectifiable curves, integral along an oriented curve, fundamental Cauchy theorem, proof applying green’s theorem, Cauchy integral formula, mobius transformation, fixed points, inverse points and critical mappings, conformal mappings






5th Semester
Revised Syllabus of Mathematics
For
Three year Degree Course ( Major Course) Paper-M502

Unit1:Definition and examples of metric  spaces, neighbourhoods, limit points, interior points, open and closed sets, closure and interior, equivalent metrics, subspace of a metric space, Cauchy sequences, completeness, Cantor’s intersection theorem.              
Unit2: Dense subsets, Baire’s category theorem, separable, second countable and first countable spaces, continuous functions, extension theorem, uniform continuity,isometry and homeomorphism.                                                                                              
Unit3:   Compactness, sequential compactness, totally bounded spaces, finite intersection property, continuous functions and compact sets, connectedness, components, continuous functions and connected sets.                                                                               

 Unit4: Definition and examples of topological spaces, metric topology, closed sets, closure, Kuratoski closure operator and neighbourhood systems, dense subsets, neighbourhoods, interior, exterior and boundary, accumulation points and derived sets, bases and sub bases, subspaces and relative topology, continuous functions and homeomorphism.                                                                                                


Unit5: Definition and examples of normed linear spaces, Banach spaces, inner product spaces and Hilbert space, some elementary properties.                                       




5th Semester
Revised Syllabus of Mathematics
For
Three year Degree Course ( Major Course) Paper-M503



Unit1:Section of a sphere by a plane, spherical triangles, properties of spherical and polar triangles, fundamental formulae of spherical triangles, sine formula, cosine formula, sine- cosine formula, cot formula, Napier’s rule of circular parts.                              

Unit2: The standard( or geometric) celestial sphere, system of coordinates, conversion of one coordinate system to the another system, diurnal motion of heavenly bodies, sidereal time, solar time(mean), rising and setting of stars, circumpolar star, dip of the horizon,
rate of change of zenith distance and azimuth, examples.                                  

Unit3: Planetary motion: annual motion of the sun, planetary motion, synodic period, orbital period,Keplar’s law of planetary motion, deduction of Keplar’s law from Newton’s law of gravitation, the equation of the orbit, velocity of a planet in its orbit, components of linear velocity perpendicular to the radius vector and to the major axis, direct and retrograde motion in a plane, laws of refraction: refraction for small zenith distance, general formula for refraction,Cassini’s hypothesis, differential equation for
refraction, effect of refraction on sunrise, sunset, right ascension and declination, shape of the disc of the sun.                                                                                           

Unit4: Geocentric parallax, parallax of the moon, right ascension and declination,
parallax on zenith distance and azimuth, stellar or annual parallax, effect of parallax on the star longitude, and latitude, effect of stellar parallax on right ascension and declination.
Lunar eclipses section of the shadow cone at moon’s geocentric distance, condition of lunar eclipse in terms of it, solar eclipses, the angle subtended at the earth’s center by the


centers of the sun and the moon at the beginning or end of a solar eclipse, condition of solar eclipse in terms of this angle, idea of ecliptic limits, frequency of eclipses.




.
5th Semester
Revised Syllabus of Mathematics
For
Three year Degree Course ( Major Course) Paper-M504



Unit1: Moments and products of inertia, parallel axes theorem, theorem of six constants, the momental ellipsoid, equimomental systems, principle axes.                       
Unit2: D’Alembert’s principle, the general equation of motion of a rigid body, motion of the centre of inertia and motion relative to the centre of inertia.                        
Unit3: Motion about a fixed axis, the compound pendulum, centre of percussion.
Unit4: Motion of a body in two dimension under finite and impulsive forces.  10 marks 
Unit5: Conservation of momentum and energy, generalized coordinates, LaGrange’s equations, initial motions.                                                                                      







5th  Semester

Revised Syllabus of Mathematics
For
Three year Degree Course ( Major Course) Paper-M505



Unit1: Random experiment, sample space , events, classical definition of probability and the theorems of total and compound probability based on this definition, axiomatic approach to the notion of probability, important theorems based on this approach, conditional probability and independent events, Bay’s theorem.                        
Unit2:Random variables, discrete and continuous probability distributions, probability function and distribution function, probability mass function and probability density function, joint distributions, marginal distribution, independent random variables, change of variables, conditional distribution.                                                              

Unit3: Mathematical expectation, basic theorems on expectation(proofs required only in case of discrete random variables), variance and standard deviation, moments and moment generating functions, covariance conditional expectation and conditional variance, Chebyshev’s inequality, law of large numbers.                                  


Unit4: Some important probability distributions: Binomial, Poisson and Normal.



5th Semester

Revised Syllabus of Mathematics
For
Three year Degree Course ( Major Course) Paper-M506

Optimization Theory Marks :
Unit1: Partitioning of matrices, simultaneous equations, basic solution, point sets, lines and hyper planes, convex sets and their properties, convex functions, convex cones.

Unit2: General linear programming problems, mathematical formulation of a linear programming problem, linear programming problem in matrix notation, feasible solution, basic solution, degenerate basic solution, necessary and sufficient condition for the existence of non-degenerate basic solution, graphical method for the solution of a linear programming problem.                                                                                        

Unit3: simplex method: fundamental theorem of linear programming problem, basic feasible solution from feasible solution, determination of improved basic feasible
solution, optimality conditions, alternative optimal solution, conditions for alternative optimal solution, theory and application of the simplex method of solution of a linear programming problem, Charne’s M-technique, two phase method.                   

Unit4:Principles of duality in linear programming problem, fundamental duality theorem, simple problems.                                                                                                   
Unit5:The Transportation  and Assignment problem.                                         




No comments:

Powered by Blogger.