{"id":33,"date":"2021-08-28T09:02:51","date_gmt":"2021-08-28T09:02:51","guid":{"rendered":"https:\/\/blog.metu.edu.tr\/sdag\/?page_id=33"},"modified":"2022-06-11T19:26:10","modified_gmt":"2022-06-11T16:26:10","slug":"numerical-methods-by-maple","status":"publish","type":"page","link":"https:\/\/blog.metu.edu.tr\/sdag\/teaching\/numerical-methods-by-maple\/","title":{"rendered":"NUMERICAL METHODS BY MAPLE"},"content":{"rendered":"

ERROR ANALYSIS<\/strong>
\nMaclaurin series of the exponential function: File_1_1<\/a>
\nRound-off error: File_1_2<\/a>
\nTaylor series expansion of cos(x): File_2_1<\/a><\/p>\n

ROOTS OF EQUATIONS<\/strong>
\nGraphical method: File_3_1<\/a>
\nBisection method: File_3_2<\/a>
\nRoot of sin(x) = x^2: File_3_3<\/a>
\nFixed-point iteration: File_4_1<\/a>
\nRoot of sin(sqrt(x)) – x = 0: File_4_2<\/a>
\nNewton-Raphson method for a single equation: File_4_3<\/a>
\nNewton-Raphson method for a system of two equations: File_4_4<\/a>
\nRoots of the system: (x=y+x^2-0.5; y=x^2-5xy): File_4_5<\/a><\/p>\n

LINEAR ALGEBRAIC EQUATIONS<\/strong>
\nNaive Gauss elimination: File_5_1<\/a>
\nGauss-Seidel iterative solver: File_6_1<\/a><\/p>\n

OPTIMIZATION<\/strong>
\nGolden-section search for maximum of a function: File_7_1<\/a><\/p>\n

CURVE FITTING<\/strong>
\nLinear regression: File_8_1<\/a>
\nPolynomial regression: File_8_2<\/a>
\nNewton’s interpolating polynomials: File_9_1<\/a>
\nLagrange’s interpolating polynomials: File_9_2<\/a>
\nCubic splines: File_9_3<\/a><\/p>\n

NUMERICAL DIFFERENTIATION AND INTEGRATION<\/strong>
\nIntegration commands in MAPLE: File_10_1<\/a>
\nTrapezoidal rule: File_10_2<\/a>
\nSimpson’s 1\/3 rule: File_10_3<\/a>
\nDerivation of two-point Gauss-Legendre points and weights: File_11_1<\/a>
\nMultiple application of three-point Gauss-Legendre quadrature: File_11_2<\/a><\/p>\n

ORDINARY DIFFERENTIAL EQUATIONS<\/strong>
\nEuler’s method: File_13_1<\/a>
\nNumerical results by Euler’s method: Euler.pdf<\/a>
\nHeun’s method: File_13_2<\/a>
\nNumerical results by Heun’s method: Heun.pdf<\/a>
\nRalston’s method: File_13_3<\/a>
\nNumerical results by Ralston’s method: Ralston.pdf<\/a>
\nSystem of ODEs: File_13_4<\/a>
\nNumerical results for system of ODEs: System.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

ERROR ANALYSIS Maclaurin series of the exponential function: File_1_1 Round-off error: File_1_2 Taylor series expansion of cos(x): File_2_1 ROOTS OF EQUATIONS Graphical method: File_3_1 Bisection method: File_3_2 Root of sin(x) = x^2: File_3_3 Fixed-point iteration: File_4_1 Root of sin(sqrt(x)) – x = 0: File_4_2 Newton-Raphson method for a single equation: File_4_3 Newton-Raphson method for a […]<\/p>\n","protected":false},"author":7599,"featured_media":0,"parent":26,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-33","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/sdag\/wp-json\/wp\/v2\/pages\/33","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.metu.edu.tr\/sdag\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.metu.edu.tr\/sdag\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/sdag\/wp-json\/wp\/v2\/users\/7599"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/sdag\/wp-json\/wp\/v2\/comments?post=33"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/sdag\/wp-json\/wp\/v2\/pages\/33\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/sdag\/wp-json\/wp\/v2\/pages\/26"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/sdag\/wp-json\/wp\/v2\/media?parent=33"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}