Section outline

  • Course Overview

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    • Instructor         : Abdullah Al Mamun

      Office                : Room: 505, AB-04, CSE Department , Permanent Campus

      Mobile              : 01754481294

      Email                : mamun.cse@diu.edu.bd

      Routine:

      CSE234(Numerical Methods)_PC-C

      Tuesday:         4PM-5:30 PM  (Scheduled time 01:00 PM - 02:30 PM but rescheduled to 4PM-5:30 PM )

      Wednesday: : 4 PM - 5:30 PM  (Scheduled time 01:00 PM - 02:30 PM but rescheduled to 4 PM - 5:30 PM)


      Online class : Google meeting link


    • Students must
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       Semester Calendar Summer 2020

      Semester Calender

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       Online IDE                                    Smart White Board 

      gbd  ide  board board

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       Counseling HOUR for Summer-2020

      Counselling

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      Announcements Forum

  • Course Assessment Strategy/ Reference/ Practice Booklist

    • Numerical Methods

    • resource icon
      Course Assessment Strategy/ Reference/ Practice Booklist File

      Course Rationale

      Numerical analysis, area of mathematics and computer science that creates, analyzes, and implements algorithms for obtaining numerical solutions to problems involving continuous variables. Such problems arise throughout the natural sciences, social sciences, engineering, medicine, and business. Since the mid 20th century, the growth in power and availability of digital computers has led to an increasing use of realistic mathematical models in science and engineering, and numerical analysis of increasing sophistication is needed to solve these more detailed models of the world. The formal academic area of numerical analysis ranges from quite theoretical mathematical studies to computer science issues. With the increasing availability of computers, the new discipline of scientific computing, or computational science, emerged during the 1980s and 1990s. The discipline combines numerical analysis, symbolic mathematical computations, computer graphics, and other areas of computer science to make it easier to set up, solve, and interpret complicated mathematical models of the real world.

       

      Course Objective

      The aim of this course is to teach the students’ different numerical methods which are essential in many areas of modern life. This course will develop their programming knowledge and analysis ability of the underlying mathematics in popular software packages. From this course, students’ will learn:

      ·         Computing integrals and derivatives

      ·         Solving differential equations

      ·         Building models based on data, be it through interpolation, Least Square,  

                or other methods

      ·         Root finding and numerical optimization

      ·         Estimating the solution to a set of linear and nonlinear equations

      ·         Computational geometry

      Course Outcomes (CO’s)

      CO1

      Solve differential equations that arises in the field of engineering and interpret the result.

      CO2

      Estimate  errors in calculation of various methods

      CO3

      Develop codes and analyze its efficiency level

      CO4

      Explain numerical procedures that are used in developing different software packages

      CO5

      Apply knowledge and skills to optimize a problem  

       

      Program Outcomes (PO’s)

      CO-PO Mapping

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      CO’s

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      PO12

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      Grading Scheme:

      Attendance-                                             07
      Quiz               -                                          15
      Assignment-                                            05
      Presentation-                                          08
      Mid -Term Exam-                                    25
      Final Exam-                                              40
      ---------------------------------------------------------------------
      Total-                                                       100




    • resource icon
      Course Outline File
    • book icon
      Text_Book
      Students must
      View

       Introductory methods of numerical analysis by S.S. Sastry

    • folder icon
      Folder of Reference Books

      1.    Numerical Analysis by Burden & Faires , current edition
      2.    Numerical Methods in Engineering, J. Kiusalaas ,Cambridge University Press


    • CSE234(Google Classroom Code=6l6cxc2)  


  • Week#01:Error Discussion , SLE and Bisection Method

    Error types

             Common way to express error:    

                

  • Week#02: Newton Raphson Method for Algebraic and Transcendental equation

    Newton Raphsom method

    Root finding of a transcendental equation by Newton-Raphson Method

  • Week #03: Newton's Forward and Backward Interpolation Formula

    Picture


  • Week #04:False Position and Fixed Point Iterative Methods

    False position 

    • Students must
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      Topics for discussion: 

      •   False position method to solve algebraic and transcendental equations with Algorithm.
      •   Fixed point iterative method to solve algebraic and transcendental equations   with Algorithm.

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      Learning Outcomes: 

      • Method of False Position:- An algorithm for finding roots which retains that prior estimate for which the function value has opposite sign from the function value at the current best estimate of the root. In this way, the method of false position keeps the root bracketed

      • The existence of a fixed point is therefore of paramount importance in several areas of mathematics and other sciences. Fixed point results provide conditions under which maps have solutions. The theory itself is a beautiful mixture of analysis (pure and applied), topology, and geometry.


    • Lesson#01: False Position Method

    • page icon
      Algorithm -False Position Method_Lecture_Note Page

      False Position Method: Link

    • resource icon
      False Position Method_Lecture_Note File
      Students must
      Mark as done

      False Position Method_Lecture_Note PDF File  

    • url icon
      Regula Falsi Method_Video#01 URL
    • url icon
      Regula Falsi Method_Video#02 URL

    • Lesson#02: Fixed Point Iterative method

    • resource icon
      Fixed-Point Iterative Method_Lecture_Note File
      Students must
      Mark as done

      Fixed-Point Iterative Method_Lecture_Note PDF File  

    • url icon
      Fixed Point Iterative method_Video#01 URL

    • url icon
      Fixed Point Iterative method_Video#02 URL
    • url icon
      Fixed Point Iterative method_Video#03 URL
    • lesson icon
      Practice Lesson on Algebraic and Transcendental equation by False-Position and Fixed Point Iterative Methods
      Students must
      Mark as done

      Students will practice the problems and share their solution at the forum

    • quiz icon
      Quiz on for PC-A

      Quiz on False- Position method and Fixed Point Iterative method

      Not available unless: You belong to PC-A Section
    • quiz icon
      Quiz on for PC-B

      Quiz on False- Position method and Fixed Point Iterative method

      Not available unless: You belong to PC-B Section
    • forum icon
      Forum on Week # 4 discussion

      Students are allowed to discuss your topic goals and objectives of Week #04

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      +Feedback

         Feedback Form  

  • Week#05: Lagrange Interpolation and, Maximum and Minimum value of a tabulated functions

    Lagrange


  • Week #06: Jacobs method and Gauss Seidal Iteration Method

    jacobs

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      Topics For Discussion: 

      o   Jacobs Iteration method

      o   Gauss-Seidal Iteration method 

      Expected Learning Outcomes: 

      o   Gauss-Seidel Method is used to solve the linear system Equations. This method is named after the German Scientist Carl Friedrich Gauss and Philipp Ludwig Siedel. It is a method of iteration for solving  n linear equation   with the unknown variables. This method is very simple and uses in digital computers for computing.

      o Jacobi iterative method is considered as an iterative algorithm which is used for determining the solutions for the system of linear equations in numerical linear algebra, which is diagonally dominant. In this method, an approximate value is filled in for each diagonal element.

    • resource icon
      Jacobs method_Lecture_Note#01 File

      Jacobs method_Lecture Note PDF File

    • resource icon
      Jacobs method_Lecture_Note#02 File

      Jacobs method_Lecture Note PDF File

    • url icon
      Jacob Method Video#01 URL
      Students must
      Mark as done
    • url icon
      Jacobs Method Video#02 URL

    • resource icon
      Gauss Seidal Iteration Method_Lecture_Note File

      Gauss Seidal Iteration Method_Lecture_Note PDF File


    • page icon
      Gauss Seidal Iteration Method-Link_Page
      Students must
      Mark as done

      Gauss Seidal Iteration Method-Link_Page for exercises


    • url icon
      Gauss Seidal Iteration Method_Video#01 URL
      Students must
      Mark as done
    • url icon
      Gauss Seidal Iteration Method_Video#02 URL
      Students must
      Mark as done
    • quiz icon
      Quiz on Jacobs method and Gauss Seidal Iteration Method-PC-A
      Not available unless: You belong to PC-A Section
    • quiz icon
      Quiz on Jacobs method and Gauss Seidal Iteration Method-PC-B
      Not available unless: You belong to PC-B Section
    • forum icon
      Forum: Discussion on week#06 Lessons
      Students must
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      Students are allowed to discuss about week#06 Lessons 

    • Students must
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      +Feedback

         Feedback Form  

  • Week #7 Midterm exam

    midterm

    Mid-Term Syllabus:

    1.  Week 1: Error Discussion , SLE and Bisection Method  
    2.  Week 2: Newton Raphson Method for Algebraic and Transcendental equation 
    3.  Week 3: Newton's Forward and Backward Interpolation Formula 
    4.  Week 4: False Position and Fixed Point Iterative Methods 

    Visit the following links for short review and Learn most important and basic concepts for midterm preparation. 

    Types of Error Analysis in Numerical Method || Part 1

     https://www.youtube.com/watch?v=-yZT5DdwBmw

    Error Analysis in Numerical Method - 1

    https://www.youtube.com/watch?v=HxnA3FrGQV8

    Error Analysis in Numerical Method - 2

    https://www.youtube.com/watch?v=HtBRdRV4mnA

    Bisection Method || Problem Solving  -1

    https://www.youtube.com/watch?v=sC2TpiQXzq0

    Bisection Method || Problem Solving  - 2

    https://www.youtube.com/watch?v=N8dwKnrKBQ0

  • Week#08: Curve Fitting

    curve fitting

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      Topics for Discussion:

      o Curve fitting: Least square method for linear and non-linear case

      Expected Learning Outcomes:

      o Construct a curve or mathematical function that has the best fit to a series of data points.

      o Curve fitting, also known as regression analysis, is used to find the "best fit" line or curve for a series of data points. Most of the time, the curve fit will produce an equation that can be used to find points anywhere along the curve.  


    • resource icon
      Curve Fitting-Lecture_Note File
    • url icon
      Curve Fitting-Lecture-Video#01 URL
      Students must
      Mark as done

    • url icon
      Curve Fitting-Lecture-Video#02 URL
      Students must
      Mark as done

      Curve Fitting for Parabola 

    • url icon
      Curve Fitting-Lecture-Video#03 URL
      Students must
      Mark as done

      Curve Fitting for exponential equation

    • forum icon
      Forum: Discussion on Curve Fitting
      Students must
      Mark as done
    • Students must
      Mark as done

      +Feedback

         Feedback Form  

  • Week#09: Divided difference interpolation

    divided difference

       Topics for Discussion:

          o Divided difference interpolation

          o Divided difference extrapolation

       Expected Learning Outcomes:

          o Newton's divided difference interpolation formula is a interpolation technique used when the interval  
             difference is not same for all sequence of values 

          o Extrapolation is an estimation of a value based on extending a known sequence of values or facts beyond 
             the area that is certainly known. In a general sense, to extrapolate is to infer something that is not explicitly  
             stated from existing information. 

  • Week #10: Runge kutta method

    Runge Kutta

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      Topics for Discussion:

      o Numerical solution of ordinary differential equations: Runge-kutta method of fourth order

      Expected Learning Outcomes:

      o Solve a differential equation using an appropriate numerical method

      o Runge–Kutta method is an effective and widely used method for solving the initial-value problems of differential equations. Runge–Kutta method can be used to construct high order accurate numerical method by functions' self without needing the high order derivatives of functions.  


    • resource icon
      Runge kutta method fourth order-Lecture_Note File
       Runge kutta method fourth order-Lecture_Note PDF File
    • url icon
      Runge Kutta_Class record : 22/07/2020 URL
      Students must
      Mark as done
    • url icon
      Runge kutta method-Video#02 URL
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      Mark as done

    • url icon
      Runge kutta method-Video#03 URL
      Students must
      Mark as done
    • url icon
      Runge kutta method-Video#04 URL
      Students must
      Mark as done
    • url icon
      Runge kutta method-Video#05 URL
      Students must
      Mark as done
    • forum icon
      Forum on Discussion

      Discussion and Problems Finding on Runge Kutta and Factorization Method 

    • Students must
      Mark as done

      +Feedback

         Feedback Form  

    • assign icon
      Assignment on Runge Kutta Method
      Students must
      Mark as done

  • Week # 11:Numerical Integration and Derivatives

    Numerical Integration


    • Students must
      Mark as done

      Topics for Discussion:

      o Numerical Integration for trapezoidal formula, Simpson’s 1/3 rule, Simpson’s 3/8 rule

      o Numerical Derivatives 

      Expected Learning Outcomes:

      o Calculate a definite integral using an appropriate numerical method

      o Numerical integration is used to evaluate a definite integral when there is no closed-form expression for the integral or when the explicit function is not known and the data is available in tabular form only.

      o Numerical differentiation describes algorithms for estimating the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.

    • resource icon
      Numerical Integration_Lecture_Note File

      Numerical Integration_Lecture_Note PDF File

    • url icon
      Numerical Integration_Video#01 URL
      Students must
      Mark as done
    • url icon
      Numerical Integration_Video#02 URL
      Students must
      Mark as done
    • url icon
      Numerical Integration_Video#03 URL
      Students must
      Mark as done
    • url icon
      Numerical Integration_Video#04 URL
      Students must
      Mark as done

    • url icon
      Numerical Integration_Video#05 URL
      Students must
      Mark as done
    • url icon
      Numerical Integration_Video#06 URL
      Students must
      Mark as done
    • url icon
      Numerical Integration_Video#07 URL
      Students must
      Mark as done
    • resource icon
      Numerical Derivatives_Lecture_Note File
      Numerical Derivatives_Lecture_Note PDF File
    • url icon
      Numerical Derivatives_Video#01 URL
      Students must
      Mark as done
    • assign icon
      Assignment on Numerical Integration and Derivatives
      Students must
      Mark as done
    • forum icon
      Forum for Discussion , Question and Answer

      At this forum all of the students including the teacher can discuss, question and answer regarding this week.

    • Students must
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      +Feedback

         Feedback Form  

  • Week#12: Factorization

    LU

    • Students must
      Mark as done

      Topics for Discussion:

      o Lower-Upper Factorization (LU Factorization)

      Expected Learning Outcomes:

      o LU decomposition is a better way to implement Gauss elimination, especially for repeated solving a number of  equations with the same left-hand side. This provides the motivation for LU decomposition where a matrix A is written as a product of a lower triangular matrix L and an upper triangular matrix U. 

    • resource icon
      Factorization-Lecture_Note File

      Factorization-Lecture_Note PDF File

    • url icon
      Factorization-Video URL
      Students must
      Mark as done

    • assign icon
      Assignment on Factorization
      Students must
      Mark as done
    • Students must
      Mark as done

      +Feedback

         Feedback Form  

    • quiz icon
      Quiz-2
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      Mark as done

  • Week 13: Final Exam

    final

    • Students must
      Mark as done

      Topics for Final Exam

      1.  Week 01: Error Discussion , SLE and Bisection Method  
      2.  Week 02: Newton Raphson Method for Algebraic and Transcendental equation 
      3.  Week 03: Newton's Forward and Backward Interpolation Formula 
      4.  Week 04: False Position and Fixed Point Iterative Methods 
      5.  Week 05: Lagrange Interpolation and, Maximum and Minimum value of a  tabulated functions
      6.  Week 06: Jacobs method and Gauss Seidal Iteration Method 
      7.  Week 08: Curve Fitting 
      8.  Week 09: Divided difference interpolation 
      9.  Week 10: Runge kutta method
      10.  Week 11: Numerical Integration and Derivatives 
      11.  Week 12: Factorization 
      Note: Midterm syllabus will be added with Final topics for final examination. 

    • Students must
      Mark as done

      +Teaching evaluation 

         Feedback Form  

    • assign icon
      ABAM_CSE234_PC-C_Final Assignment
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      Mark as done
    • assign icon
      Presentation Assignment
      Students must
      Mark as done