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  4. MTH603 - Numerical Analysis
  5. MTH603 Assignment 1 Solution and Discussion
dy/dx - = 1 - y,y(0) = 0 is an example of
L
dy dx = 1 - y,y(0) = 0 is an example of Answer An ordinary differential equation A partial differential equation A polynomial equation None of the given choices
MTH603 - Numerical Analysis
In Double integration, the interval [a, b] should be divided into [c, d) should be divided into --sub intervals of size k. --subintervals of size h and the interval
zaasmiZ
In Double integration, the interval [a, b] should be divided into [c, d) should be divided into --sub intervals of size k. --subintervals of size h and the interval Answer equal, equal equal, unequal unequal, equal unequal, unequal
MTH603 - Numerical Analysis
The (n + 1) th difference of a polynomial of degree n is...
Kevin AustinK
The (n + 1) th difference of a polynomial of degree n is… Answer 0 Constant n +1
MTH603 - Numerical Analysis
Let P be any real number and h be the step size of any interval. Then the relation between h and P for the backward difference is given by
G
Let P be any real number and h be the step size of any interval. Then the relation between h and P for the backward difference is given by Answer x-x, = Ph x- x, = P x + x, = Ph (x - x,)h= P
MTH603 - Numerical Analysis
In integrating $\int_{0}^{\frac{2}{2}} \cos x d x$ by dividing the interval into four equal parts, width of the interval should be
zaasmiZ
In integrating $\int_{0}^{\frac{2}{2}} \cos x d x$ by dividing the interval into four equal parts, width of the interval should be Answer $\frac{\pi}{2}$ $\pi$ $\frac{\pi}{8}$
MTH603 - Numerical Analysis
In fourth order Runge-Kutta method K 4
zaasmiZ
In fourth order Runge-Kutta method K 4 is given by Answer k4 = hf(xn th,yn + kz) k4 = hf(xn + 2h, + 2kz) None of the given choices k4 = hf(x, — h,Yn — kz)
MTH603 - Numerical Analysis
In fourth order Runge-Kutta method k2
zaasmiZ
In fourth order Runge-Kutta method k2 is given by Answer ^2-“/”“” З’Уп 3’ k2 = 45(-12.30-42)
MTH603 - Numerical Analysis
What is the Process of finding the values outside the interval (Xo,x,) called?
zaasmiZ
What is the Process of finding the values outside the interval (Xo,x,) called? Answer interpolation iteration Polynomial equation extrapolation
MTH603 - Numerical Analysis
When we apply Simpson's 3/8 rule, the number of intervals n must be
zaasmiZ
When we apply Simpson’s 3/8 rule, the number of intervals n must be Answer Even Odd Multiple of 3 Page 177 Similarly in deriving composite Simpson’s 3/8 rule, we divide the interval of integration into n sub-intervals, where n is divisible by 3, and applying the integration formula Multiple of 8
MTH603 - Numerical Analysis
Milne's P-C method is a multi step method where we assume that the solution to the given initial value problem is known at past --equally spaced points.
zaasmiZ
Milne’s P-C method is a multi step method where we assume that the solution to the given initial value problem is known at past –equally spaced points. Answer 2 1 3 4 1
MTH603 - Numerical Analysis
The truncation error in Adam's predictor formula is ....-times more than that in corrector formula
zaasmiZ
The truncation error in Adam’s predictor formula is …-times more than that in corrector formula Answer 10 11 12 13
MTH603 - Numerical Analysis
To apply Simpson's 3/8 rule, the number of intervals be
zaasmiZ
Answer 10 11 12 13
MTH603 - Numerical Analysis
Which formula is useful in finding the interpolating polynomial?
zaasmiZ
Given the following data Which formula is useful in finding the interpolating polynomial? Answer Lagrange’s interpolation formula X 1 2 5 9 f(x) 2 0 30 132 Page 135 Newton’s forward difference interpolation formula Newton’s backward difference interpolation formula None of the given choices
MTH603 - Numerical Analysis
Rate of change of any quantity with respect to another can be modeled by
zaasmiZ
Answer An ordinary differential equation A partial differential equation A polynomial equation None of the given choices
MTH603 - Numerical Analysis
Romberg's integration method is ------ than Trapezoidal and Simpson's rule.
zaasmiZ
Answer more accurate less accurate equally accurate none of the given choices
MTH603 - Numerical Analysis
In integrating f, e2* dx by dividing into eight equal parts, width of the interval should be......
zaasmiZ
Answer 0.250 0.500 0.125 0.625
MTH603 - Numerical Analysis
To apply Simpson's 1/3 rule, valid number of intervals are?
zaasmiZ
7 8 5 3 Page 177 The Simpson’s 1/3 rule, we have used two sub-intervals of equal width. In order to get a composite formula, we shall divide the interval of integration [a, b] Into an even number
MTH603 - Numerical Analysis
Newton's divided difference interpolation formula is used when the values of the independent variable are
zaasmiZ
Equally spaced Not equally spaced Constant None of the above
MTH603 - Numerical Analysis
If there are (n+1) values of y corresponding to (n+1) values of x, then we can represent the function f(x) by a polynomial of degree
zaasmiZ
If there are (n+1) values of y corresponding to (n+1) values of x, then we can represent the function f(x) by a polynomial of degree
MTH603 - Numerical Analysis
MTH603 Assignment 1 Solution and Discussion
cyberianC
Re: MTH603 Assignment 1 Solution and Discussion Assignment No. 1 MTH603 (Spring 2022) Total Marks: 20 Due Date: 8th June, 2022 DON’T MISS THESE: Important instructions before attempting the solution of this assignment: • To solve this assignment, you should have good command over 1-8 lectures. • Upload assignments properly through the LMS, No Assignment will be accepted through email. • Write your ID on the top of your solution file. Don’t use colored backgrounds in your solution files. Use Math Type or Equation Editor, etc. for mathematical symbols. You should remember that if the solution files of some students are finding the same (copied), we will reward zero marks to all those students. Make a solution by yourself and protect your work from other students, otherwise both original and copied assignments will be awarded zero marks. Also remember that you are supposed to submit your assignment in Word format, any other format like scanned images, etc. will not be accepted and be awarded zero marks Question 1 Find a real root of the equation 2x+cos⁡(x)+e^x=0 using Bisection Method using Newton Raphson Method Also compare the results and comment which of the methods performs better and which is worst. You will consider x_0=-0.6557 as a best approximation while comparing the roots. Note: In each of the above methods,you are required to perform three iterations. Spring 2022_MTH603_1.docx
MTH603 - Numerical Analysis

MTH603 Assignment 1 Solution and Discussion

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mth603assignment 1 solutionspring 2022solution and discussion
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  • cyberianC cyberian

    Re: MTH603 Assignment 1 Solution and Discussion

    Assignment No. 1 MTH603 (Spring 2022)

    Total Marks: 20
    Due Date: 8th June, 2022

    DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
    • To solve this assignment, you should have good command over 1-8 lectures.
    • Upload assignments properly through the LMS, No Assignment will be accepted through email.
    • Write your ID on the top of your solution file.
    Don’t use colored backgrounds in your solution files.
    Use Math Type or Equation Editor, etc. for mathematical symbols.
    You should remember that if the solution files of some students are finding the same (copied), we will reward zero marks to all those students.
    Make a solution by yourself and protect your work from other students, otherwise both original and copied assignments will be awarded zero marks.
    Also remember that you are supposed to submit your assignment in Word format, any other format like scanned images, etc. will not be accepted and be awarded zero marks

    Question 1

    Find a real root of the equation 2x+cos⁡(x)+e^x=0
    using Bisection Method
    using Newton Raphson Method
    Also compare the results and comment which of the methods performs better and which is worst.
    You will consider x_0=-0.6557 as a best approximation while comparing the roots.

    Note:
    In each of the above methods,you are required to perform three iterations.

    Spring 2022_MTH603_1.docx

    cyberianC Offline
    cyberianC Offline
    cyberian
    Cyberian's Cyberian's Gold
    wrote on last edited by
    #2

    @cyberian said in MTH603 Assignment 1 Solution and Discussion:

    Find a real root of the equation 2x+cos⁡(x)+e^x=0
    using Bisection Method

    619c84d5-1907-4412-b8ed-a6ccaa0c7382-image.png
    6fa9899d-e90a-447a-ac6d-29140faeb3c6-image.png
    b8b4d3f0-e5cf-4f5b-83b0-5ed3d24f2c62-image.png

    Discussion is right way to get Solution of the every assignment, Quiz and GDB.
    We are always here to discuss and Guideline, Please Don't visit Cyberian only for Solution.
    Cyberian Team always happy to facilitate to provide the idea solution. Please don't hesitate to contact us!
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    • cyberianC cyberian

      Re: MTH603 Assignment 1 Solution and Discussion

      Assignment No. 1 MTH603 (Spring 2022)

      Total Marks: 20
      Due Date: 8th June, 2022

      DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
      • To solve this assignment, you should have good command over 1-8 lectures.
      • Upload assignments properly through the LMS, No Assignment will be accepted through email.
      • Write your ID on the top of your solution file.
      Don’t use colored backgrounds in your solution files.
      Use Math Type or Equation Editor, etc. for mathematical symbols.
      You should remember that if the solution files of some students are finding the same (copied), we will reward zero marks to all those students.
      Make a solution by yourself and protect your work from other students, otherwise both original and copied assignments will be awarded zero marks.
      Also remember that you are supposed to submit your assignment in Word format, any other format like scanned images, etc. will not be accepted and be awarded zero marks

      Question 1

      Find a real root of the equation 2x+cos⁡(x)+e^x=0
      using Bisection Method
      using Newton Raphson Method
      Also compare the results and comment which of the methods performs better and which is worst.
      You will consider x_0=-0.6557 as a best approximation while comparing the roots.

      Note:
      In each of the above methods,you are required to perform three iterations.

      Spring 2022_MTH603_1.docx

      cyberianC Offline
      cyberianC Offline
      cyberian
      Cyberian's Cyberian's Gold
      wrote on last edited by
      #3

      @cyberian said in MTH603 Assignment 1 Solution and Discussion:

      using Newton Raphson Method

      cb5f43b7-f199-43a4-99af-9618aced0ea6-image.png
      a988082b-ec2c-4983-bd43-6225af9060f8-image.png
      53da29b8-dca4-4667-8b78-792185860a4c-image.png
      0b35ec17-4800-45f7-8713-b0e546ff4707-image.png

      Discussion is right way to get Solution of the every assignment, Quiz and GDB.
      We are always here to discuss and Guideline, Please Don't visit Cyberian only for Solution.
      Cyberian Team always happy to facilitate to provide the idea solution. Please don't hesitate to contact us!
      [NOTE: Don't copy or replicating idea solutions.]
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      • cyberianC cyberian has marked this topic as solved on
      • cyberianC Offline
        cyberianC Offline
        cyberian
        Cyberian's Cyberian's Gold
        wrote on last edited by
        #4

        MTH603-Assignment-1-Spring-2022

        Discussion is right way to get Solution of the every assignment, Quiz and GDB.
        We are always here to discuss and Guideline, Please Don't visit Cyberian only for Solution.
        Cyberian Team always happy to facilitate to provide the idea solution. Please don't hesitate to contact us!
        [NOTE: Don't copy or replicating idea solutions.]
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        • cyberianC Offline
          cyberianC Offline
          cyberian
          Cyberian's Cyberian's Gold
          wrote on last edited by
          #5

          Spring 2023_MTH603_1 Solution

          Discussion is right way to get Solution of the every assignment, Quiz and GDB.
          We are always here to discuss and Guideline, Please Don't visit Cyberian only for Solution.
          Cyberian Team always happy to facilitate to provide the idea solution. Please don't hesitate to contact us!
          [NOTE: Don't copy or replicating idea solutions.]
          Quiz Copy Solution
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          • cyberianC Offline
            cyberianC Offline
            cyberian
            Cyberian's Cyberian's Gold
            wrote on last edited by
            #6

            Only students of Section: Nabeela Wali shall solve this Assignment.
            Assignment # 01 MTH603 (Spring 2024)
            Marks: 10
            Due Date: May 6, 2024
            DON’T MISS THESE: Important instructions before attempting the solution and submission of this assignment:
            ⚫ Lectures 3-10 are encompassed in Assignment 1.
            ⚫ Only students in Section: Nabeela Wali shall complete this Assignment.
            ⚫ Students in other teacher’s section will be completing a different assignment and are strictly prohibited from solving this one.
            ⚫ Submitting a copied assignment or irrelevant assignment will result in a zero grade.
            ⚫ Assignment 1 is due on May 6, 2024.
            ⚫ Properly Upload the solution of this assignment in MS Word format on LMS as per the previous practice.
            Question 1 5 Marks
            Find a root of the equation 𝑥3 − 3𝑥 − 5 = 0, in the interval (2,3) using Bisection Method after three Iterations.
            Note: Accuracy up to four decimal places is required.
            Question 2 5 Marks
            Find a root of the following equation in the interval (0,1) using Newton-Raphson Method after three iterations
            𝑥𝑒𝑥 − cos 𝑥 = 0
            Take Initial value 0.5.
            Note: Accuracy up to four decimal places is required. Here is a transcendental equation all the calculation should be done in the radians mode.

            Discussion is right way to get Solution of the every assignment, Quiz and GDB.
            We are always here to discuss and Guideline, Please Don't visit Cyberian only for Solution.
            Cyberian Team always happy to facilitate to provide the idea solution. Please don't hesitate to contact us!
            [NOTE: Don't copy or replicating idea solutions.]
            Quiz Copy Solution
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            cyberianC 1 Reply Last reply
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            • cyberianC cyberian

              Only students of Section: Nabeela Wali shall solve this Assignment.
              Assignment # 01 MTH603 (Spring 2024)
              Marks: 10
              Due Date: May 6, 2024
              DON’T MISS THESE: Important instructions before attempting the solution and submission of this assignment:
              ⚫ Lectures 3-10 are encompassed in Assignment 1.
              ⚫ Only students in Section: Nabeela Wali shall complete this Assignment.
              ⚫ Students in other teacher’s section will be completing a different assignment and are strictly prohibited from solving this one.
              ⚫ Submitting a copied assignment or irrelevant assignment will result in a zero grade.
              ⚫ Assignment 1 is due on May 6, 2024.
              ⚫ Properly Upload the solution of this assignment in MS Word format on LMS as per the previous practice.
              Question 1 5 Marks
              Find a root of the equation 𝑥3 − 3𝑥 − 5 = 0, in the interval (2,3) using Bisection Method after three Iterations.
              Note: Accuracy up to four decimal places is required.
              Question 2 5 Marks
              Find a root of the following equation in the interval (0,1) using Newton-Raphson Method after three iterations
              𝑥𝑒𝑥 − cos 𝑥 = 0
              Take Initial value 0.5.
              Note: Accuracy up to four decimal places is required. Here is a transcendental equation all the calculation should be done in the radians mode.

              cyberianC Offline
              cyberianC Offline
              cyberian
              Cyberian's Cyberian's Gold
              wrote on last edited by cyberian
              #7

              @cyberian said in MTH603 Assignment 1 Solution and Discussion:

              Question 1 5 Marks
              Find a root of the equation 𝑥3 − 3𝑥 − 5 = 0, in the interval (2,3) using Bisection Method after three Iterations.
              Note: Accuracy up to four decimal places is required.

              Screen Shot 2024-05-03 at 7.11.17 PM.png
              Screen Shot 2024-05-03 at 7.14.44 PM.png Screen Shot 2024-05-03 at 7.15.21 PM.png Screen Shot 2024-05-03 at 7.15.36 PM.png Screen Shot 2024-05-03 at 7.15.48 PM.png Screen Shot 2024-05-03 at 7.16.07 PM.png Screen Shot 2024-05-03 at 7.16.21 PM.png Screen Shot 2024-05-03 at 7.17.18 PM.png Screen Shot 2024-05-03 at 7.17.26 PM.png

              Download Source File

              MTH603 - Assignment 1 - Spring 2024 - Nabeela Wali - Solution file.pdf

              Discussion is right way to get Solution of the every assignment, Quiz and GDB.
              We are always here to discuss and Guideline, Please Don't visit Cyberian only for Solution.
              Cyberian Team always happy to facilitate to provide the idea solution. Please don't hesitate to contact us!
              [NOTE: Don't copy or replicating idea solutions.]
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              1 Reply Last reply
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              • zaasmiZ Offline
                zaasmiZ Offline
                zaasmi
                Cyberian's Gold
                wrote on last edited by
                #8

                Assignment # 01 MTH603 (Summer 2024)
                Marks: 10
                Due Date: 21.09 2024
                DON’T MISS THESE: Important instructions before attempting the solution and
                submission of this assignment:
                 Lectures 23-30 are encompassed in Assignment 1.
                 Assignment 1 is due on 21 September 2024.
                 Properly Upload the solution of this assignment in MS Word format on
                LMS as per the previous practice.
                Question 1 [Marks 5]
                First construct the divided difference table and then find the interpolating
                polynomial of the following function 𝑦 = 𝑓(𝑥) by Newton’s Divided Difference
                Formula.
                𝑥 0 𝜋
                𝜋
                2
                𝑦 = 𝑓(𝑥) 0 1 0
                Question 2 [Marks 5]
                Compute 𝑓′(1.5), from the following tabular data using the forward difference
                formula for derivative.
                𝑥 1.5 2.0 2.5 3.0 3.5 4.0
                𝑓(𝑥) 3.375 7.000 13.625 24.000 38.875 59.000

                Summer 2024_MTH603_1.pdf

                Discussion is right way to get Solution of the every assignment, Quiz and GDB.
                We are always here to discuss and Guideline, Please Don't visit Cyberian only for Solution.
                Cyberian Team always happy to facilitate to provide the idea solution. Please don't hesitate to contact us!
                [NOTE: Don't copy or replicating idea solutions.]
                VU Handouts
                Quiz Copy Solution
                Mid and Final Past Papers
                Live Chat

                cyberianC 1 Reply Last reply
                0
                • zaasmiZ zaasmi

                  Assignment # 01 MTH603 (Summer 2024)
                  Marks: 10
                  Due Date: 21.09 2024
                  DON’T MISS THESE: Important instructions before attempting the solution and
                  submission of this assignment:
                   Lectures 23-30 are encompassed in Assignment 1.
                   Assignment 1 is due on 21 September 2024.
                   Properly Upload the solution of this assignment in MS Word format on
                  LMS as per the previous practice.
                  Question 1 [Marks 5]
                  First construct the divided difference table and then find the interpolating
                  polynomial of the following function 𝑦 = 𝑓(𝑥) by Newton’s Divided Difference
                  Formula.
                  𝑥 0 𝜋
                  𝜋
                  2
                  𝑦 = 𝑓(𝑥) 0 1 0
                  Question 2 [Marks 5]
                  Compute 𝑓′(1.5), from the following tabular data using the forward difference
                  formula for derivative.
                  𝑥 1.5 2.0 2.5 3.0 3.5 4.0
                  𝑓(𝑥) 3.375 7.000 13.625 24.000 38.875 59.000

                  Summer 2024_MTH603_1.pdf

                  cyberianC Offline
                  cyberianC Offline
                  cyberian
                  Cyberian's Cyberian's Gold
                  wrote on last edited by cyberian
                  #9

                  @zaasmi said in MTH603 Assignment 1 Solution and Discussion:

                  Assignment # 01 MTH603 (Summer 2024)
                  Marks: 10
                  Due Date: 21.09 2024
                  DON’T MISS THESE: Important instructions before attempting the solution and
                  submission of this assignment:
                   Lectures 23-30 are encompassed in Assignment 1.
                   Assignment 1 is due on 21 September 2024.
                   Properly Upload the solution of this assignment in MS Word format on
                  LMS as per the previous practice.
                  Question 1 [Marks 5]
                  First construct the divided difference table and then find the interpolating
                  polynomial of the following function 𝑦 = 𝑓(𝑥) by Newton’s Divided Difference
                  Formula.
                  𝑥 0 𝜋
                  𝜋
                  2
                  𝑦 = 𝑓(𝑥) 0 1 0
                  Question 2 [Marks 5]
                  Compute 𝑓′(1.5), from the following tabular data using the forward difference
                  formula for derivative.
                  𝑥 1.5 2.0 2.5 3.0 3.5 4.0
                  𝑓(𝑥) 3.375 7.000 13.625 24.000 38.875 59.000

                  Summer 2024_MTH603_1.pdf

                  Download

                  Discussion is right way to get Solution of the every assignment, Quiz and GDB.
                  We are always here to discuss and Guideline, Please Don't visit Cyberian only for Solution.
                  Cyberian Team always happy to facilitate to provide the idea solution. Please don't hesitate to contact us!
                  [NOTE: Don't copy or replicating idea solutions.]
                  Quiz Copy Solution
                  Mid and Final Past Papers
                  WhatsApp Channel
                  Mobile Tax Calculator

                  zaasmiZ 1 Reply Last reply
                  0
                  • cyberianC cyberian

                    @zaasmi said in MTH603 Assignment 1 Solution and Discussion:

                    Assignment # 01 MTH603 (Summer 2024)
                    Marks: 10
                    Due Date: 21.09 2024
                    DON’T MISS THESE: Important instructions before attempting the solution and
                    submission of this assignment:
                     Lectures 23-30 are encompassed in Assignment 1.
                     Assignment 1 is due on 21 September 2024.
                     Properly Upload the solution of this assignment in MS Word format on
                    LMS as per the previous practice.
                    Question 1 [Marks 5]
                    First construct the divided difference table and then find the interpolating
                    polynomial of the following function 𝑦 = 𝑓(𝑥) by Newton’s Divided Difference
                    Formula.
                    𝑥 0 𝜋
                    𝜋
                    2
                    𝑦 = 𝑓(𝑥) 0 1 0
                    Question 2 [Marks 5]
                    Compute 𝑓′(1.5), from the following tabular data using the forward difference
                    formula for derivative.
                    𝑥 1.5 2.0 2.5 3.0 3.5 4.0
                    𝑓(𝑥) 3.375 7.000 13.625 24.000 38.875 59.000

                    Summer 2024_MTH603_1.pdf

                    Download

                    zaasmiZ Offline
                    zaasmiZ Offline
                    zaasmi
                    Cyberian's Gold
                    wrote on last edited by
                    #10

                    @cyberian said in MTH603 Assignment 1 Solution and Discussion:

                    @zaasmi said in MTH603 Assignment 1 Solution and Discussion:

                    Assignment # 01 MTH603 (Summer 2024)
                    Marks: 10
                    Due Date: 21.09 2024
                    DON’T MISS THESE: Important instructions before attempting the solution and
                    submission of this assignment:
                     Lectures 23-30 are encompassed in Assignment 1.
                     Assignment 1 is due on 21 September 2024.
                     Properly Upload the solution of this assignment in MS Word format on
                    LMS as per the previous practice.
                    Question 1 [Marks 5]
                    First construct the divided difference table and then find the interpolating
                    polynomial of the following function 𝑦 = 𝑓(𝑥) by Newton’s Divided Difference
                    Formula.
                    𝑥 0 𝜋
                    𝜋
                    2
                    𝑦 = 𝑓(𝑥) 0 1 0
                    Question 2 [Marks 5]
                    Compute 𝑓′(1.5), from the following tabular data using the forward difference
                    formula for derivative.
                    𝑥 1.5 2.0 2.5 3.0 3.5 4.0
                    𝑓(𝑥) 3.375 7.000 13.625 24.000 38.875 59.000

                    Summer 2024_MTH603_1.pdf

                    Download

                    Discussion is right way to get Solution of the every assignment, Quiz and GDB.
                    We are always here to discuss and Guideline, Please Don't visit Cyberian only for Solution.
                    Cyberian Team always happy to facilitate to provide the idea solution. Please don't hesitate to contact us!
                    [NOTE: Don't copy or replicating idea solutions.]
                    VU Handouts
                    Quiz Copy Solution
                    Mid and Final Past Papers
                    Live Chat

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