LILAC

Reminder Theorem Statement : if f(x) is a polynomial of degree m in x, then the reminder in the division of f(x) by x-α is equal to f(x) . Proof : By Euclid ’s or division algorithm we can find, the polynomial q(x) and r(x) such that f(x)=(x-α)q+r(x) . Where either r(x)=0 or the degree of r(x) is less than g(x)(x-α) . Therefore r(x)=0 or the degree of r(x) is less than “1” or will be equal to “0” . In the second case r(x)=k(constant) i) f(x)=(x-α)q(x)+k   put x=α   (x)=(α-α)q(x)+k  f(α)=k ; Factor theorem If “α”  is   the root f(x)=0 then x-α is  factor of f(x) Proof:   f(x)=(x-α)q(x)+k --> (1) Put x=α  , f(α)=k Put f(α)=0 ,   “α” is a root of the equation f(x)=0 => k=0 ; Substituting => f(x)=(x-α)q(x) v  x-α is a factor of f(x) ; Fundamental theorem of Algebra Every polynomial equation of degree n ≥ 1 has at least one or real or imaginary. Synthetic  division for finding quotient and remainder for dividing a polyno

HAPPY 33rd ANNIVERSARY OF MONGOLIAN MAN LAUNCHED INTO SPACE ! !!  Монголчууд бид нар амны хишигтэй, азтай, хиймортой ард түмэн шүү ! ,, хятадуудаас түрүүлээд сансарт ниссэн  A Mongolian man was launched into space for the first time on Marc h 22, 1981. Citizen of Mongolia Gurragchaa Jugderdemid and Vladimir Janibekov of the Russia were launched to space from Baikonur space site in a Soyuz-39 spaceship. In space they joined two other Soviet space cosmonauts and spent 7 days 20 hours and 42 minutes there. Two Mongolian cosmonauts were prepared in 1978 to work in space under the Intercosmos program. J.Gurragchaa was chosen to fly and Maidarjavyn Ganzorig was left as Gurragchaa’s backup pilot. We introduce the conversation and reminiscence of the two men who reported on the preparations and launching of the flight on the occasion of 33 years of launching a Mongol man to space. We are the 10th nation who ever defeated earths gravity or 2nd nation in asia who did that. Mission statistic

1-р курсд байхдаа тэмдэглэж авч байсан  бичилтүүдийг хувын дэвтэрнээсээ оруулж байгаа болно. Theory of equation  If  a 0, a 1, a 2………….. an -1 a n  are integers then an expression of the form     a 0 x n +a 1 x n-1 +……….+a n . called a polynomial of degree  n ≥  in the              variable “x”,   if a≠ 0. Eg: -6x+y=0 , x 2 +x+1=0 , 6x 2 +3x+2=0 A polynomial of degree one is of the form ax+b=c a polynomial of degree two is of the form ax 2 +bx+c=0 and so on.  Equality of 2 polynomials Two polynomial f(x) and g(x) are said to equal if they are of same degree and the co-efficient corresponding powers are of  “x”  are equal. Eg: f(x)=a 0 x n +a 1 x n-1 +….+a n        g(x)=b 0 y m +b 0 y m-1 +….+b m the value of a polynomial if f(x) is equal to ax 0 +a 1 x+…+a n is a polynomial of degree n then f(x)=a 0 α+α 1 x n-1 +….+α n is called the value of the polynomial f(x) at  x= α . ·        if   f(x)=2x-7x+8                  f(0)=8   Zeros of polyn

  B.Sc degree for 3 years  under university of Mysore Syllabus of  Mathematics  Year Semester topics I I Algebra, Analytical Geometry and Calculus-1 I II Algebra, Analytic Geometry and Calculus-1 II III Calculus-1 II IV Algebra and differential equations III V Paper-A-  Calculus-2 Paper –B-  Algebra and Calculus Paper-C-  Applied mathematics III VI Paper-D- Numerical Analysis and Vector Calculus Paper-E- Linear Algebra Paper-F-  Complex Analysis

Би Энэтхэг улсад  Майсури их сургуулийг  (Mysore university) шинжлэх ухааны бакалавраар төгссөн.Миний төрсөн эх орон минь Монгол бол сурч, амьдарч  дассан газар минь Энэтхэг орон.                     http://uni-mysore.ac.in/about-the-university/