Chidambaram Ramanujam | | | Top of FormBottom of Form | | | | | Before we look at the life and work of Chidambaram Padmanabhan Ramanujam we must warn the reader that this article is on Ramanujam‚ NOT Ramanujan the number theorist who worked with G H Hardy (there is only a difference of one letter in their names!). Ramanujam’s father was C S Padmanabhan who was an advocate working in Madras‚ India‚ at the High Court. C P Ramanujam was educated in Madras‚ first at Ewart’s School‚ where
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Random Variables....................................................................... 33 8. Binomial Random Variable ...................................................................... 37 9. The Poisson and Hypergeometric Random Variables............................ 44 10. Continuous Random Variables: Uniform and Normal....................... 46 11. Sampling Distributions and Central Limit Theorem.......................... 55 12. Confidence Interval for a Population Mean ................
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for linear programming‚ Math. Programming‚ 43 (1989)‚ pp. 209-223. linear (1991)‚ pp [3] R.W. COTTLE‚ J. S. PANG‚ AND R. E. STONE‚ The linear complementarity problem‚ Academic Press‚ Boston‚ 1992. [4] G. DE GHELLINCK AND J.-PH. VIAL‚ A polynomial Newton method for linear programming‚ Algorithmica‚ 1 (1986)‚ pp [5] A. V. FIACCO AND G. P. MCCORMICK‚ Nonlinear Programming: Sequential Unconstrained Minimization Techniques‚ John Wiley‚ New York 1968 and SIAM‚ Philadelphia‚ 1990. Tokyo‚ Japan‚ 1992. CA
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this paper is 80. This document consists of 15 printed pages and 1 blank page. © UCLES 2012 [Turn over 2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation ax2 + bx + c = 0‚ x= − b ± b 2 − 4ac . 2a Binomial Theorem n (a + b)n = an + an–1 b + 1 n n–2 2 a b +…+ 2 n n! . where n is a positive integer and = r (n − r )! r! 2. TRIGONOMETRY Identities sin2 A + cos2 A = 1. sec2 A = 1 + tan2 A. cosec2
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the product of the charges‚ and inversely proportional to the square of the distance between the centers of the two charges. In mathematical vector notation Coulomb’s Law is expressed as where Fr is the force on particle 1 due to particle 2 in Newtons‚ q is the charge on 12 1 particle 1 in Coulombs‚ q2 is the charge on particle 2 in Coulombs‚ rˆ12 is a unit vector originating at the center of particle 1 and pointing directly away from particle 2‚ r is the distance between the centers of the two
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following; a) Binomial Distribution - is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments‚ each of which yields success with probability p. Therewith the probability of an event is defined by its binomial distribution. A success/failure experiment is also called a Bernoulli experiment or Bernoulli trial; when n = 1‚ the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical
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can mean[1]: * Use of letters and symbols to represent values and their relations‚ especially for solving equations. This is also called "Elementary algebra". Historically‚ this was the meaning in pure mathematics too‚ like seen in "fundamental theorem of algebra"‚ but not now. * In modern pure mathematics‚ * a major branch of mathematics which studies relations and operations. It’s sometimes called abstract algebra‚ or "modern algebra" to distinguish it from elementary algebra.
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Invertible matrix From Wikipedia‚ the free encyclopedia (Redirected from Nonsingular matrix) Jump to: navigation‚ search In linear algebra an n-by-n (square) matrix A is called invertible (some authors use nonsingular or nondegenerate) if there exists an n-by-n matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case‚ then the matrix B is uniquely determined by A and is called the inverse of A‚
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The Greek Society The Greek ways of life‚ including its cities and religion‚ introduced some of the cultural models that we still follow today. Greece’s art‚ science‚ and military structure personified and made the success of the empire possible. This advanced society flourished in its golden age shortly after defeating Persia in many wars. These Greco-Persian wars included the first clash of civilizations‚ and the struggle between the man-centered universe and the God-centered universe. The Greek
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Methods – LU Decomposition from Gauss Elimination – Solution of Tridiagonal systems – Solution of Linear Systems. Eigen values‚ Eigen vectors – properties – Condition number of Matrix‚ Cayley – Hamilton Theorem (without proof) – Inverse and powers of a matrix by Cayley – Hamilton theorem – Diagonalization of matrix – Calculation of powers of matrix – Model and spectral matrices. Real Matrices‚ Symmetric‚ skew symmetric‚ Orthogonal‚ Linear Transformation - Unit-III Linear Transformations
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