Monday, September 1, 2008

SET EXAM - Mathematics Paper III (Unit 7-15)

7. Topology:
Elements of Topological Spaces, Continuity, Convergence, Homeomorphism, Compactness, Connectedness, Separation Axioms, First and Second Countability, Separability, Subspaces, Product Spaces, quotient spaces. Tychonoff's Theorem, Urysohn's Metrization theorem, Homotopy and Fundamental Group.
8.Discrete Mathematics:
Partially ordered sets, Lattices, Complete Lattices, Distributive lattices, Complements, Boolean Algebra, Boolean Expressions, Application to switching circuits, Elements of Graph Theory, Eulerian and Hamiltonian graphs, planar Graphs, Directed Graphs, Trees, Permutations and Combinations, Pigeonhole principle, principle of Inclusion and Exclusion, Derangements.
9.Ordinary and Partial Differential Equations:
Existence and Uniqueness of solution dy/dx =f(x,y) Green's function, sturm Liouville Boundary Value Problems, Cauchy Problems and Characteristics, Classification of Second Order PDE, Separation of Variables for heat equation, wave equation and Laplace equation, Special functions.
10.Number Theory:
Divisibility; Linear diophantine equations. Congruences. Quadratic residues; Sums of two squares, Arithmetic functions Mu, Tau, Phi and Sigma ( and ).
11.Mechanics:
Generalised coordinates; Lagranges equation; Hamilton's cononical equations; Variational principles - Hamilton's principles and principles of least action; Two dimensional motion of rigid bodies; Euler's dynamical equations for the motion of rigid body; Motion of a rigid body about an axis; Motion about revolving axes.
12.Elasticity:
Analysis of strain and stress, strain and stress tensors; Geometrical representation; Compatibility conditions; Strain energy function; Constitutive relations; Elastic solids Hookes law; Saint-Venant's principle, Equations of equilibrium; Plane problems - Airy's stress function, vibrations of elastic, cylindrical and spherical media.
13.Fluid Mechanics:
Equation of continuity in fluid motion; Euler's equations of motion for perfect fluids; Two dimensional motion complex potential; Motion of sphere in perfect liquid and motion of liquid past a sphere; vorticity; Navier-Stokes's equations for viscous flows-some exact solutions.
14.Differetial Geometry:
Space curves - their curvature and torsion; Serret Frehat Formula; Fundamental theorem of space curves; Curves on surfaces; First and second fundamental form; Gaussian curvatures; Principal directions and principal curvatures; Goedesics, Fundamental equations of surface theory.
15.Calculus of Variations:
Linear functionals, minimal functional theorem, general variation of a functional, Euler- Lagrange equation; Variational methods of boundary value problems in ordinary and partial differential equations.

9 comments:

Anonymous said...

Your blog keeps getting better and better! Your older articles are not as good as newer ones you have a lot more creativity and originality now keep it up!

Anonymous said...

Just want to say what a great blog you got here!
I've been around for quite a lot of time, but finally decided to show my appreciation of your work!

Thumbs up, and keep it going!

Cheers
Christian, iwspo.net

Anonymous said...

Do you mind if I quote a couple of your articles as
long as I provide credit and sources back to
your blog? My blog site is in the very same area
of interest as yours and my visitors would truly benefit from a lot of the information you provide
here. Please let me know if this alright with you. Appreciate it!



Feel free to surf to my website - reviewed quantrim

Anonymous said...

Your work is always to get factors completed effectively, correctly,
and cost-effectively. So, it truly is often greater to decide on a theme then do the
holiday decorations. It will be to a small degree time-consuming, nonetheless
it can even be a good work for 1 individual inside your loved ones to try
out and do who maybe isn't that gifted at decorating.

Feel free to surf to my page ... martha stewart christmas decorating tips

Anonymous said...

Because the admin of this web site is working, no hesitation very rapidly it will be well-known,
due to its quality contents.

my blog; buy Phen375 uk

Anonymous said...

Unquestionably consider that that you said. Your favourite justification appeared to be
at the net the simplest factor to take note of.
I say to you, I certainly get annoyed whilst other folks
consider concerns that they plainly don't recognize about. You managed to hit the nail upon the highest as well as defined out the whole thing with no need side effect , other people could take a signal. Will likely be again to get more. Thanks

My webpage ... activity calorie calculator

Anonymous said...

If your house has a lot of country elements to it, a Shaker-style rustic coffee table would be a nice addition.
To bring nature on your table you can also use Sweet-gum-tree
spurs,just punch the card with hole and tie in place with ribbon.
Table lamps let you pull off a great makeover for any room without having to cost a fortune.


Here is my website - modern kitchen table decor

Anonymous said...

I do not understand, some time ago nike free run 3you grab 9.9 perfume free shipping mobile power,cheap nike free shoes and I
had a whole, brought one to cheap nike free runuse, really good, calculate costs,
courier 5 nike free run 2 womensyuan, 5 yuan battery shell circuit 3 yuan pour loss, even if all wholesale, 9.9 nike free running shoesis also the
most protected. I do not know the business profits come from.





My web page; nike free run 3 shoes

Pou Hacker said...


free marvel contest of champions hacker FOR unlocking heroes of marvel contest

Subscribe via email/ Newsletter

Enter your email address:

Delivered by FeedBurner


Click here to get Sureshmath-newsletter