{"id":184,"date":"2019-12-31T08:02:13","date_gmt":"2019-12-31T08:02:13","guid":{"rendered":"https:\/\/bcisnotes.com\/thirdsemester\/?page_id=184"},"modified":"2020-03-30T04:57:59","modified_gmt":"2020-03-30T04:57:59","slug":"nm","status":"publish","type":"page","link":"https:\/\/bcisnotes.com\/thirdsemester\/nm\/","title":{"rendered":"Numerical Methods"},"content":{"rendered":"<p><strong>1. Introduction\u00a0<\/strong><br \/>\n<strong>2. Importance of numerical methods<\/strong><\/p>\n<ul>\n<li>Review of calculus<\/li>\n<li>Taylor\u2019s theorem<\/li>\n<li>Errors in numerical computations<\/li>\n<li>Use of computer programming in numerical methods<\/li>\n<\/ul>\n<p><strong>3. Solution of Nonlinear Equations<\/strong><\/p>\n<ul>\n<li>Nonlinear equations and their solutions<\/li>\n<li>Trial and error method<\/li>\n<li>Graphical method<\/li>\n<li>Iterative methods: Bisection method<\/li>\n<li>False position method<\/li>\n<li>Secant method<\/li>\n<li><a href=\"https:\/\/bcisnotes.com\/thirdsemester\/numerical-methods\/newtons-method\/\" target=\"_blank\" rel=\"noopener noreferrer\">Newton\u2019s method<\/a><\/li>\n<li>Rate of convergence of iterative methods<\/li>\n<li>Newton\u2019s method for polynomials and Horner\u2019s rule<\/li>\n<\/ul>\n<p><strong>4. Solution of Set of Algebraic Equations<\/strong><\/p>\n<ul>\n<li>Existence of solutions for linear set of equations<\/li>\n<li>Gaussian elimination method<\/li>\n<li>pivoting<\/li>\n<li>ill- conditioning<\/li>\n<li>Gauss-Jordan method<\/li>\n<li>Matrix inversion<\/li>\n<li>Matrix factorization: Doolittle algorithm<\/li>\n<li>Cholesky&#8217;s factorization<\/li>\n<li>Iterative solution using Gauss Seidel method<\/li>\n<li>Eigen value and eigen vector using power method<\/li>\n<\/ul>\n<p><strong>5. Interpolation and Approximation<\/strong><\/p>\n<ul>\n<li><strong>\u00a0<\/strong>Lagrange interpolation<\/li>\n<li>Newton\u2019s interpolation using divided differences and difference table<\/li>\n<li>Cubic spline interpolation<\/li>\n<li>Least squares method of fitting linear and nonlinear function for given data<\/li>\n<\/ul>\n<p><strong>6. Numerical Differentiation and Integration\\<\/strong><\/p>\n<ul>\n<li>\u00a0Numerical differentiation formulas<\/li>\n<li>Maxima and minima of a tabulated function<\/li>\n<li>Newton- Cote\u2019s quadrature formulas: Trapezoidal<\/li>\n<li>Simpson\u2019s 1\/3 and 3\/8 rule<\/li>\n<li>Romberg integration<\/li>\n<li>Gaussian integration<\/li>\n<\/ul>\n<p><strong>7. Solution of Ordinary Differential Equations\u00a0<\/strong><\/p>\n<ul>\n<li>Review of differential equations<\/li>\n<li>Initial value problem<\/li>\n<li>Taylor series method<\/li>\n<li>Euler&#8217;s method and its accuracy<\/li>\n<li>Henu&#8217;s method<\/li>\n<li>Runge-Kutta methods<\/li>\n<li>Solution of higher order equations<\/li>\n<li>Solution of boundary value problems using finite difference and Shooting method<\/li>\n<\/ul>\n<p><strong>8. Solution of Partial Differential Equations\u00a0<\/strong><\/p>\n<ul>\n<li>Review of partial differential equations<\/li>\n<li>Deriving difference equations<\/li>\n<li>Solution of Laplacian equation and Poisson&#8217;s equation<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<div class=\"mh-excerpt\"><p>1. Introduction\u00a0 2. Importance of numerical methods Review of calculus Taylor\u2019s theorem Errors in numerical computations Use of computer programming in numerical methods 3. Solution <a class=\"mh-excerpt-more\" href=\"https:\/\/bcisnotes.com\/thirdsemester\/nm\/\" title=\"Numerical Methods\">[&#8230;]<\/a><\/p>\n<\/div>","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Numerical Methods - BCIS<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/bcisnotes.com\/thirdsemester\/nm\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Numerical Methods - BCIS\" \/>\n<meta property=\"og:description\" content=\"1. Introduction\u00a0 2. 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