Numerical presentation

2.  Presentated by :
 Names:
Md. Habibur Rahman

3. Life and works of
Johann Carl Friedrich
Gauss
He was born on April 30, 1777, to
a peasant couple in Brunswick, in
what is now western Germany. He
was died in 23 february 1855
(aged 77)
He was a German mathematician
who contributed significantly to
many fields, including number
theory, algebra, statistics, analysis,
differential geometry, geodesy,
geophysics, mechanics,
electrostatics, astronomy, matrix

4.  At the age of seven started
elementary school, and his
potential was noticed almost
immediately. In 1788 Gauss began
his education at the Gymnasium
with the help of Buttner and
Bartels, where he learnt high
German and Latin. Then he
entered Brunswick Collegium
Carolinum and left it to study at
“Gottingen University”. In 1799
he received a degree in
Brunswick.

5.  In 1832 after Gauss and Weber
finished producing a a geodesic
survey of Hanover began
investigating the theory of
terrestrial magnetism and
electricity
 Gauss made many discoveries
including the discovery that there
can never be a magnetic
monopole, that is to say, there can
never be a magnet with only one
pole

6.  He came to this conclusion because
he understood that magnetic field
lines are always in a closed loop
unlike electrical field lines.
 Gauss's work can be used to
determine the magnetic flux at the
surface of a symmetrical object
where the charge is uniformly spread
over the surface of that object. Gauss
used his research to derive other
important fundamental ideas about
electricity and magnetism.

7. When Einstein thought about the
nature of space and time he realised
that space the correct Geometry of
our universe is a hyperbolic
geometry (non-euclidean geometry)
which is a 'curved' one. Many
present-day cosmologists feel that
we live in a three dimensional
universe that is curved into the 4th
dimension and that Einstein's
theories were proof of this.

8.  Hyperbolic Geometry plays a
very important role in the
Theory of General Relativity
so Gauss and his friends who
developed early models of
non-euclidean geometry made
their contributions to
Einstein's work on relativity.

9. Gauss Elimination Method
Gauss elimination method’s purpose is to find the
solution’s to a linear syestem.It is used to convert
syestems to an upper traingular form.
The fundamental idea is to add multiples of one equation
to the others in order eliminate a variable and to continue
this process until only one variable is left .
Once this final variable determined,it’s value is
substituted back into the other questions in order to
evaluate the remaining unknowns .

10. Gauss Elimination Method
We have now eliminated the x term from the last two questions. Now
simplify the last two questions dividing by 2 and 3,respectively:
x-3y+z=4
0x-y+3z=-5
0x-5y-3z=11
To eliminate the y term in the last question,multiply the second
question by -5 and add it to the third question:We have now eliminated
the x term from the last two questions. Now simplify the last two
questions dividing by 2 and 3,respectively:
x-3y+z=4
0x-y+3z=-5
0x-5y-3z=11
To eliminate the y term in the last question,multiply the second
question by -5 and add it to the third question:

11.  Every polynomial equation having
complex coefficients and degree ≥ 1
has at least one complex root. It is
equivalent to the statement that a
polynomial p(z) of degree n has
values z1 for which p(zi) = 0 . Such
values are called polynomial roots. An
example of a polynomial with a single
root of multiplicity> 1 is,
 Z^2- 2z+1=(z-1)(z-1) which has z=1
as a root of multiplicity 2.

12.  Vertical least squares
fitting proceeds by
finding the sum of the
squares of the vertical
deviations R^2 of a set
of
 The standard errors for a and b are

13.  He did not want any of his sons to go into mathematics or
science for “fear of sullying the family name”
 Perfectionist and diligent worker; told his wife was dying,
supposedly said, “tell her to wait a moment till I’m done”
 Made many discoveries which he never published
 Preferred to not show intuition of proofs – wanted them to
appear “out of thin air”

14.  Fellow of the Royal Society at 1804
 Lalande Prize(1810)was an award for scientific advances in
astronomy
 Fellow of the Royal Society of the Edinburgh at 1820
 Copley Medal(1838) is a scientific award given by the Royal
Society, London, for "outstanding achievements in research in
any branch of science.