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#### Numerical Analysis (Code 09050503)

 S.No. Content of the topics Learning  Objectives Teaching Guidelines Methodology Time                         (Hours) 1 1.Finite difference operators and their relations Student will be able to understand about finite difference operators and interpolation Lecture should be effective so that student will be able to grasp the topics easily Assignments/ Seminars/     Class Tests/ Presentations 10 2.Finiding the missing terms and effect of error in a difference tabular values 3.Interpolation with equal intervals: Newton’s forward and Newton’s backward interpolation formulae 4.Interpolation with unequal intervals: Newton’s divided difference 5.Lagrange’s interpolation formulae 6.Hermite formula 2 1.Central Differences: Gauss forward and Gauss’s backward interpolation formulae Student will be able to understand the study of Central differences, distributions Lecture should be effective so that student will be able to grasp the topics easily Assignments  /Seminars  /Class Tests /presentations 15 2.Sterling, Bessel Formula 3.Probability distribution of random variables 4.Binomial distribution 5.Poisson’s distribution 6.Normal distribution: Mean, Variance and Fitting 3 1.Numerical differentiation: Derivative of a function using interpolation formulae as studied in section-I &II Student will be able to know about the numerical differentiation Lecture should be effective so that student will be able to grasp the topics easily Assignments/ Seminars/     Class Tests/ Presentations 12 2.Eigen value Problems: Power method, Jacobi’s method 3.Given’s method, House Holder’s method 4.QR method, Lanczos method 4 1.Numerical integration: Newton’s Cote’s Quadrature formula Student will be able to understand the numerical integration and numerical solutions of ODEs with methods Lecture should be effective so that student will be able to grasp the topics easily Assignments/ Seminars/     Class Tests/ Presentations 2.Trapezoidal rule, Simpon’s one-third and three-eigth rule 3.Chebyehev formula, Gauss Quadratic formula 4.Numerical solution of ODEs: Single-step methods-Picard’s method, Taylor’s series method