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### Title Numerical Analysis (Code 09010603)

 S.No Unit Contents Learning Objective Teaching Guidelines Methodology Time (Hrs) 1 One 1. Finite difference operators and their relations 2. Finiding the missing terms and effect of error in a difference tabular values 3. Interpolation with equal intervals 4. Interpolation with unequal intervals 5. Lagrange’s interpolation formulae, Hermite formula Students will be able to   To study the difference operators, and Interpolation with equal and unequal intervals Lecture should be so effective so that the students can grasp the topic easily Lecture Seminar Discussion Assignments Seminar Class Tests 10 2 Two ·   Central Differences: Gauss forward and Gauss’s backward interpolation formulae ·   Sterling, Bessel Formula ·   Probability distribution of random variables, Binomial, Poisson’s and Normal distribution ·   Numerical differentiation: Derivative of a function using interpolation formulae as studied in section-I &II ·   Eigen value Problems: Power method, Jacobi’s method ·   Given’s method, House Holder’s method ·   QR method, Lanczos method Students will be able to       Understand Central difference interpolation,  Differentiation of functions with numerical values and Eigen value and Eigen vectors Lecture should be so effective so that the students can grasp the topic easily Lecture Seminar Discussion Assignments Seminar Class Tests Evaluation of Assignements 20 3 Three ·   Numerical integration: Newton’s Cote’s Quadrature formula ·   Trapezoidal, Simpon’s one-third and three-eigth rule ·   Chebyehev formula, Gauss Quadratic formula ·   Numerical solution of ODEs: Single-step methods-Picard’s method, Taylor’s series method ·   Euler’s method, Runge-Kutta method ·   Modified Euler’s method ·   Milne-Simpson’s method Students will be able to     Understand Numerical integration and Numerical solutions of ODEs with different methods Lecture should be so effective so that the students can grasp the topic easily Lecture Seminar Discussion Assignments Seminar Class Tests Evaluation of Assignements 15