{"id":7250,"date":"2026-01-20T09:48:35","date_gmt":"2026-01-20T02:48:35","guid":{"rendered":"https:\/\/istiarto.staff.ugm.ac.id\/?page_id=7250"},"modified":"2026-06-18T10:55:39","modified_gmt":"2026-06-18T03:55:39","slug":"numerical-methods","status":"publish","type":"page","link":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/kuliah\/sarjana-s1\/numerical-methods\/","title":{"rendered":"Numerical Methods"},"content":{"rendered":"\r\n

Numerical Methods is a course subject in the IUP\u2019s Civil Engineering. It is a 2-credit compulsory subject in the fourth semester. The subject covers the following topics.<\/p>\r\n

    \r\n
  1. Introduction\r\n
      \r\n
    1. Mathematics in civil engineering<\/li>\r\n
    2. Spreadsheet, computer programs<\/li>\r\n
    3. Approximations and round-off errors<\/li>\r\n<\/ol>\r\n<\/li>\r\n
    4. Roots of equations\r\n
        \r\n
      1. Graphical methods<\/li>\r\n
      2. The bisection methods<\/li>\r\n
      3. The false-position methods<\/li>\r\n
      4. Simple fixed-point iteration<\/li>\r\n
      5. The Newton-Raphson method<\/li>\r\n
      6. The secant method<\/li>\r\n
      7. Multiple roots<\/li>\r\n<\/ol>\r\n<\/li>\r\n
      8. Linear algebraic equations\r\n
          \r\n
        1. The graphical method<\/li>\r\n
        2. Cramer’s rule<\/li>\r\n
        3. Elimination of unknowns<\/li>\r\n
        4. Naive Gauss elimination<\/li>\r\n
        5. Gauss-Jordan<\/li>\r\n
        6. LU<\/em> decomposition<\/li>\r\n
        7. The matrix inverse<\/li>\r\n
        8. Jacobi<\/li>\r\n
        9. Gauss-Seidel<\/li>\r\n
        10. Successive over-\/under-relaxation<\/li>\r\n
        11. Tri-diagonal matrix, Thomas algorithm<\/li>\r\n
        12. Symmetric matrix, Cholesky decomposition<\/li>\r\n<\/ol>\r\n<\/li>\r\n
        13. Curve fitting\r\n
            \r\n
          1. Least-squares regression<\/li>\r\n
          2. Interpolation<\/li>\r\n
          3. Fourier approximation<\/li>\r\n<\/ol>\r\n<\/li>\r\n
          4. Numerical differentiation and integration\r\n
              \r\n
            1. The trapezoidal rule<\/li>\r\n
            2. Simpson’s rule<\/li>\r\n
            3. Gauss quadrature<\/li>\r\n<\/ol>\r\n<\/li>\r\n
            4. Ordinary differential equations (initial-value problems)\r\n
                \r\n
              1. Euler’s method<\/li>\r\n
              2. Heun’s method<\/li>\r\n
              3. The midpoint (improved polygon) method<\/li>\r\n
              4. Runge-Kutta methods<\/li>\r\n
              5. Stiffness<\/li>\r\n
              6. Multistep methods<\/li>\r\n<\/ol>\r\n<\/li>\r\n
              7. Introduction to the finite difference approximation (boundary-value problems)\r\n
                  \r\n
                1. Boundary-value problems<\/li>\r\n
                2. Eigenvalue problems<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n

                  Reference<\/h2>\r\n

                  Chapra, S.C., Canale, R.P., 2015, Numerical Methods for Engineers<\/em>, 7th Ed., McGraw-Hill Book Co., New York.<\/p>\r\n

                  Weekly Agenda<\/h2>\r\n\r\n
                  \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
                  Week#<\/strong><\/td>\r\nSubject<\/strong><\/td>\r\nDescription<\/b><\/span><\/td>\r\n<\/tr>\r\n<\/thead>\r\n
                  1<\/td>\r\nIntroduction<\/td>\r\n\r\n
                    \r\n
                  • Course description<\/li>\r\n
                  • Mathematics in civil engineering<\/li>\r\n
                  • Spreadsheet and computer programs<\/li>\r\n
                  • Approximation and round-off errors<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
                  2<\/td>\r\nRoots of equations (1\/2)<\/td>\r\n\r\n
                    \r\n
                  • Graphical methods<\/li>\r\n
                  • The bisection methods<\/li>\r\n
                  • The false-position methods<\/li>\r\n
                  • Simple fixed-point iteration<\/li>\r\n
                  • The Newton-Raphson method<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
                  3<\/td>\r\nRoots of equations (2\/2)<\/td>\r\n\r\n
                    \r\n
                  • The secant method<\/li>\r\n
                  • Multiple roots<\/li>\r\n
                  • Exercise #1: roots of equations<\/span><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
                  4<\/td>\r\nLinear algebraic equations (1\/3)<\/td>\r\n\r\n
                    \r\n
                  • Gauss elimination<\/li>\r\n
                  • Gauss-Jordan<\/li>\r\n
                  • LU decomposition<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
                  5<\/td>\r\nLinear algebraic equations (2\/3)<\/td>\r\n\r\n
                    \r\n
                  • The matrix inverse<\/li>\r\n
                  • Jacobi<\/li>\r\n
                  • Gauss-Seidel<\/li>\r\n
                  • Successive over-\/under-relaxation<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
                  6<\/td>\r\nLinear algebraic equations (3\/3)<\/td>\r\n\r\n
                    \r\n
                  • Tri-diagonal matrix, Thomas algorithm<\/li>\r\n
                  • Symmetric matrix, Cholesky decomposition<\/li>\r\n
                  • Exercise #2: linear algebraic equations<\/span><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
                  7<\/td>\r\nRegression<\/td>\r\n\r\n
                    \r\n
                  • Polynomial regression<\/li>\r\n
                  • Multivariable regression<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
                  8<\/td>\r\nMidterm exam<\/strong><\/span><\/td>\r\n<\/tr>\r\n
                  9<\/td>\r\nInterpolation<\/td>\r\n\r\n
                    \r\n
                  • Newton interpolation method<\/li>\r\n
                  • Lagrange interpolation method<\/li>\r\n
                  • Fourier approximation<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
                  10<\/td>\r\nNumerical differentiation and integration (1\/2)<\/td>\r\n\r\n
                    \r\n
                  • The trapezoidal rule<\/li>\r\n
                  • Simpson’s rule<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
                  11<\/td>\r\nNumerical differentiation and integration (2\/2)<\/td>\r\n\r\n
                    \r\n
                  • Gauss quadrature<\/li>\r\n
                  • Exercise #3: interpolation, numerical differentiation and integration<\/span><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
                  12<\/td>\r\nInitial-value problems (1\/3)<\/td>\r\n\r\n
                    \r\n
                  • Euler’s method<\/li>\r\n
                  • Heun’s method<\/li>\r\n
                  • The midpoint (improved polygon) method<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
                  13<\/td>\r\nInitial-value problems (2\/3)<\/td>\r\n\r\n
                    \r\n
                  • Runge-Kutta methods<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
                  14<\/td>\r\nInitial-value problems (3\/3)<\/td>\r\n\r\n
                    \r\n
                  • Stiffness<\/li>\r\n
                  • Multistep methods<\/li>\r\n
                  • Exercise #4: initial-value problems<\/span><\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
                  15<\/td>\r\nBoundary-value problems<\/td>\r\n\r\n
                    \r\n
                  • Introduction to FDA<\/li>\r\n
                  • Eigenvalue problems<\/li>\r\n<\/ul>\r\n<\/td>\r\n<\/tr>\r\n
                  16<\/td>\r\nFinal exam<\/span><\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/figure>\r\n

                  Lecture Notes<\/h2>\r\n

                  NM00_Course_Description<\/a>
                  NM01_Math_and_Civil_Eng<\/a>
                  NM02_Roots_of_Equations<\/a>
                  NM03_Linear_Algebraic_Equations<\/a>
                  NM04_Curve_Fitting<\/a><\/p>\r\n

                  Exams<\/h2>\r\n

                  Soal_UTS_Numerical_Methods_2026_IUP<\/a>
                  Soal_UAS_Numerical_Methods_2026_IUP<\/a><\/p>","protected":false},"excerpt":{"rendered":"

                  Numerical Methods is a course subject in the IUP\u2019s Civil Engineering. It is a 2-credit compulsory subject in the fourth semester. The subject covers the following topics. Introduction Mathematics in civil engineering Spreadsheet, computer programs Approximations and round-off errors Roots … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":71,"featured_media":0,"parent":2999,"menu_order":4,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-7250","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/pages\/7250","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/users\/71"}],"replies":[{"embeddable":true,"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/comments?post=7250"}],"version-history":[{"count":38,"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/pages\/7250\/revisions"}],"predecessor-version":[{"id":7442,"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/pages\/7250\/revisions\/7442"}],"up":[{"embeddable":true,"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/pages\/2999"}],"wp:attachment":[{"href":"https:\/\/istiarto.staff.ugm.ac.id\/index.php\/wp-json\/wp\/v2\/media?parent=7250"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}