Direct methods Gaussian elimination method Gaussian elimination method 6 LU decomposition by o64e0bx

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									                     ‫الجامعة :الكوفة‬                                 ‫جمهورية العراق‬
   ‫الكلية :الرياضيات وعلوم الحاسوب‬                                ‫وزارة التعليم العالي والبحث العلمي‬
                 ‫القســم :الرياضيات‬                                ‫جهاز االشراف والتقويم العلمي‬
                     ‫المرحلة :الثانية‬
‫اسم المحاضر الثالثي :انعام رزاق جبر‬
                ‫اللقب العلمي :مدرس‬
            ‫المؤهل العلمي :ماجستير‬
       ‫مكان العمل :قسم الرياضيات‬



                                        ‫جدول الدروس االسبوعي‬

                                                     ‫م.انعام رزاق جبر‬                           ‫االسم‬
                                            Inam.math@yahoo.com                     ‫البريد االلكتروني‬
                                                        )1(‫تحليل عددي‬                      ‫اسم المادة‬

       ‫مصادر الخطا وايجاد الخطا المطلق والخطا النسبي وايجاد جذور‬                         ‫مقرر الفصل‬

        ‫المعادالت الغير خطية وحل منظومة المعادالت الخطية واالندراج‬
 ‫والتفاضل العددي والتكامل العددي ,حل المعادالت الفاضلية االعتيادية‬
                                                               ‫والجزئية‬
   ‫ايجاد الحل العددي لجميع مسائل الرياضيات كإيجاد جذور المعادالت‬                        ‫اهداف المادة‬

‫الغير خطية والمعادالت التفاضلية ومنظومة المعادالت الخطية وغيرها‬
                                                    ‫من المسائل الرياضية‬
 Error sources: error analysis, round-off error, relative      ‫التفاصيل االساسية للمادة‬
 error, absolute error. Solutions of nonlinear equations:
 Determination of roots positions, the bisection method, fixed
 point iterative method, Newton-Raphson method, conditions
 and order of convergence of the methods, Aitkin's method to
 accelerate the convergence. Numerical solutions of linear
 systems: Direct methods (Gaussian elimination method, L-U
 decomposition methods), iterative methods (Jacobi, Gauss-
 Seidel and successive over relaxation methods), the
 convergence condition, ill-conditioned systems. Interpolation
 methods: Lagrange method, divided differences, forward
 backward and central differences, Newton formulas of finite
 differences, piece-wise polynomial approximation (linear and
 cubic splines).
 Numerical differentiation: Forward central and backward
 approximations of derivatives,error analysis and discussions.
‫)5891( ‪Numerical Analysis by Burden‬‬
                                                                                                           ‫الكتب المنهجية‬


‫‪1-Numerical methods by P.Kandasamy and‬‬
‫)0002( ‪K.Thilagavathy‬‬                                                                                    ‫المصادر الخارجية‬
‫‪2-Applied Numerical Analysis using Matlab, second‬‬
‫‪edotion by Laurene-v.fausett‬‬
‫االمتحان النهائي‬         ‫المشروع‬               ‫االمتحانات‬       ‫المختبر‬        ‫الفصل الدراسي‬
                                                ‫اليومية‬                                                    ‫تقديرات الفصل‬
      ‫ال‬
   ‫مث ً13%‬                   ‫-‬                    ‫ال‬
                                                ‫مث ً3%‬         ‫مثال11%‬              ‫ال‬
                                                                                 ‫مث ً35%‬


                                                                                                          ‫معلومات اضافية‬




                                  ‫الجامعة :‬                                              ‫جمهورية العراق‬
                                    ‫الكلية :‬                                          ‫وزارة التعليم العالي والبحث العلمي‬
                              ‫اسم القســم :‬                                            ‫جهاز االشراف والتقويم العلمي‬
                                  ‫المرحلة :‬
                   ‫اسم المحاضر الثالثي :‬
                            ‫اللقب العلمي :‬
                         ‫المؤهل العلمي :‬
                             ‫مكان العمل :‬


                                                          ‫جدول الدروس‬
                                                            ‫االسبوعي‬
    ‫المالحظات‬                    ‫المادة العلمية‬               ‫المادة النظرية‬                   ‫التاريخ‬
                                                                                                                     ‫االسبوع‬




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‫توقيع العميد :‬                ‫توقيع االستاذ :‬
      Republic of Iraq                                    University:kufa
The Ministry of Higher Education                          College:mathematics and
                                                          computer science
    & Scientific Research
                                                          Department:mathematics
                                                          Stage:second
                                                          Lecturer name:Inam Razaq
                                                          AL-Saiq
                                                          Academic Status:Lecturer
                                                          Qualification:master
                                                          Place of work:mathematics

                          Course Weekly Outline

Course Instructor     Inam razaq AL-Saiq
E_mail                Inam.math@yahoo.com
Title                 Numerical analysis
Course Coordinator    Error sources: error analysis, round-off error, relative error,
                      absolute error. Solutions of nonlinear equations, Numerical
                      solutions of linear system, Interpolation methods, Numerical
                      differentiation, Numerical Integration, Least square
                      approximation, First order ordinary differential equatio Higher
                      order ordinary differential equations ns, Partial differential
                      equations
                 With the present development of the computer technology ,it is
Course Objective necessary to develop efficient algorithms for solving problems in
                 science, engineering and technology. This course gives a complete
                 procedure for solving different kinds of problems that occur in
                 engineering numerically . At the end of the course the students would
                 be acquainted with the basic concepts in numerical methods and their
                 uses.




                  This is an undergraduate course on numerical analysis (1)and (2). The
Course Description
                 topics covered in this semester include: Error sourse &          Numerical
                  solutions of nonlinear equations &Numerical solutions of linear systems &
                  Interpolation methods and Numerical           differentiation,. Numerical
                  Integration, Least square approximation, First order ordinary differential
                  equatio Higher order ordinary differential equations ns, Partial
                      differential equations

                          Numerical Analysis by Burden (1985)
 Textbook

                          1-Numerical methods by P.Kandasamy and
 References               K.Thilagavathy (2000)
                          2-Applied Numerical Analysis using Matlab, second
                          edotion by Laurene-v.fausett
                          Term Tests Laboratory         Quizzes     Project      Final Exam
 Course Assessment
                           As (35%)   As (10%)          As (5%)       ----        As (50%)


 General Notes            Type here general notes regarding the course




       Republic of Iraq
                                                              University:
The Ministry of Higher Education                              College:
     & Scientific Research                                    Department:
                                                              Stage:
                                                              Lecturer name:
                                                              Academic Status:
                                                              Qualification:
                                                              Place of work:

                              Course weekly Outline
   week        Date               Topics Covered          Lab. Experiment        Notes
                                                            Assignments
     1                       error analysis,round-off          matlab
                             error, relative error,
                             absolute

     2                          1- Solutions of           Bisection method
                                   nonlinear
                                   equations:
     Determination of roots
     positions, the bisection
     method
3          fixed point                fixed
           iterative method,         point iterative
           Newton-Raphson         method, Newton-
           method                 Raphson method
4       conditions                 Aitkin's method to
           and order of               accelerate the
        convergence of the         convergence.
        methods, Aitkin's
        method to
           accelerate the
        convergence.

5    Numerical solutions of linearGaussian
     systems:                     elimination method
        Direct methods
     (Gaussian elimination
     method)
6        L-U decomposition           L-U decomposition
        methods                      methods
7         First examination         First examination
8    iterative methods             (Jacobi, Gauss-
     (Jacobi, Gauss-Seidel)       Seidel)
9        Successive over relaxation successive over
         methods), the convergence relaxation methods),
         condition,
            ill-conditioned systems.

10   Interpolation methods:        Lagrange method
        Lagrange method
11      divided differences,        divided differences,
        forward backward            forward backward
           and central                and central
     differences                differences
12   Newton formulas of         Newton formulas of
     finite differences         finite differences
13   piece-wise polynomial      piece-wise
     approximation (linear      polynomial
     and cubic splines)         approximation
                                (linear and cubic
                                splines)
14   Numerical differentiation: Numerical
       Forward central and differentiation:
     backward                       Forward central
     approximations of            and backward
     derivatives,                 approximations of
                                  derivatives,
15     Second examination         Second examination
16      Final examination          Final examination
              Half-year Break
17      Numerical Integration Numerical
       (Trapezoidal rule,     Integration
     Simpson's rule)             (Trapezoidal
                              rule, Simpson's rule)
18   mid-point rule, error    mid-point rule,
     analysis                 error analysis
19   Romberg method             Romberg method

20   opened and closed             opened and closed
     Newton-Cotes methods           Newton-Cotes
                                       methods
21         Gauss-Legendre              Gauss-
           method.                     Legendre
                                       method.


22      Least square method         Least square
                                  method
23      First examination          First examination
24      linear and nonlinear        linear and
       and exponential              nonlinear and
     approximation                  exponential
                                  approximation
25   continuous function          continuous function
     approximation.               approximation.


26      First order ordinary    First order ordinary
        differential equations: differential equations:
     Explicit and implicit      Explicit and implicit
     Euler's methods            Euler's methods
27   Taylor series method,       Taylor series
     second and fourth order    method, second and
     Runge-Kutta methods,       fourth order Runge-
     Adam-Bashforth multi-      Kutta methods,
     step methods               Adam-Bashforth
                                multi-step methods
28      Higher order ordinary Higher order
        differential equations: ordinary differential
        Boundary value          equations: Boundary
                             problems (finite          value problems (finite
                             difference method)        difference method)
29                               initial value problem    initial value
                                (the shooting method).    problem (the
                                                          shooting method).

30                              Partial differential      Partial differential
                                equations:                equations:
                                 Numerical solutions       Numerical
                             of parabolic              solutions of
                                                       parabolic
31                             Second examination      Second examination
32                              Final examination       Final examination
     Instructor Signature:                               Dean Signature:

								
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