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Real Analysis Notes by Prof Syed Gul Shah

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itive integer such that $\left| {\,{s_n}}\right|>\frac{1}{2}s$. * Theorem: Let //a// and //b// be fi... _n}{t_n}\right\}$ converges to st. (iii) $\left\{\frac{{{s_n}}}{{{t_n}}} \right\}$ converges to $\frac{s}{t}$ provided ${t_n}\ne 0\,\,\,\,\forall \,\,\,n$ and... orem: Let $a_n>0, b_n>0$ and $\lim_{n\to\infty } \frac{a_n}{b_n}=\lambda\ne 0$ then the series $\sum{a_n

Operation Research: Handwritten Notes

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1 * Method of integer programming 221 * The fractional (pure integer) algorithm 221 * Algebraic development of cuts 222 * Main steps (fractional cut method) 225 * The mixed algorithm 23... * Branch and bound method 240 * Main steps (fractional cut method) * The mixed algorithm 265

Notes for Numerical Methods by M Usman Hamid

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ation * Trapezoidal rule * Simpson’s $\left(\frac{1}{3}\right)$ rule * Simpson’s $\left(\frac{3}{8}\right)$ rule * Weddle’s * Boole’s rule * Rect