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MTH603 - Numerical Analysis

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  • MTH603 Quiz 3 Solution and Discussion

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    cyberianC

    @cyberian said in MTH603 Quiz 3 Solution and Discussion:

    which of the following points the max value of 2nd deruvative of function f(x)=-(2/x) in the inteval : [1,4] exits

    To find where the maximum value of the second derivative of the function
    𝑓
    (
    𝑥
    )

    −
    2
    𝑥
    f(x)=−
    x
    2
    ​
    exists in the interval
    [
    1
    ,
    4
    ]
    [1,4], we will first find the second derivative of the function and then determine where it achieves its maximum value within the given interval.

  • MTH603 Quiz 1 Solution and Discussion

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    cyberianC

    how many eigenvalues will exit corresponding to the function exp(ax)

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    cyberianC

    @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

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    cyberianC

    @asad-saab
    Fall 2023
    MTH603
    Assignment # 1
    Section In charge: Husna Muzaffar Total Marks 20
    Instructions

    To solve this assignment you need to have a good grip on lectures 1-15. The course is segmented into four sections, each of which is supervised by a different faculty member. Information regarding the section in charge can be
    found in the course information section on the LMS. A distinct assignment file has been given to each section, resulting in a total
    of four separate assignment files. The relevant assignment file can be downloaded from the announcement section of the course. It is important to note that students can only view the announcements relevant to their respective sections. You will prepare the solution of assignment on Word file and upload at the assignment interface on LMS as per usual practice. Plagiarism in the submitted assignment will lead to a zero grade. Additionally, any student who submits a solution file that is not applicable to their section will also get a zero grade.
    𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧# 𝟏: Marks 10 Solve the system of equations by using Crout’s method.
    2𝑥 + 5𝑦 + 3𝑧 = 16

    𝐐𝐮𝐞𝐬𝐭𝐢𝐨𝐧# 𝟐:
    Marks 10
    3𝑥 + 𝑦 + 2𝑧 = 11 −3𝑥 + 7𝑦 + 8𝑧 = 10
    Solve the following system of equations by using Jacobi′s iterative method for the first three iterations by taking initial starting of solution vector as (0,0,0). 8𝑥 − 2𝑦 − 2𝑧 = 3
    −2𝑥 + 6𝑦 + 𝑧 = 9
    −2𝑥+𝑦+7𝑧= 6

    images.png

  • MTH603 Quiz 2 Solution and Discussion

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    cyberianC

    @zaasmi said in MTH603 Quiz 2 Solution and Discussion:

    a7601db2-b0dc-4e95-bb7d-911dae9e615e-image.png

    88879c16-d2e8-48cd-abbd-e8c4036836e0-image.png

  • Mth603 midterm past papers

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  • mth603 final term solved papers by moaaz

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    zaasmiZ

    @zaasmi said in MTH603 Assignment 2 Solution and Discussion:

    @zaasmi said in MTH603 Assignment 2 Solution and Discussion:

    Assignment NO. 2 MTH603 (Spring 2021)

    Maximum Marks: 20
    Due Date: July 30, 2021

    DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
    • To solve this assignment, you should have good command over 23 - 30 lectures.
    Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in the 23-30 lectures.
    • Upload assignments properly through LMS, No Assignment will be accepted through email.
    • Write your ID on the top of your solution file.
    Don’t use colourful back grounds in your solution files.
    Use Math Type or Equation Editor Etc. for mathematical symbols.
    You should remember thatif we found the solution files of some students are same then we will reward zero marks to all those students.
    Try to make solution by yourself and protect your work from other students, otherwise you and the student who send same solution file as you will be given zero mark.
    Also remember that you are supposed to submit your assignment in Word format any other like scan images etc. will not be accepted and we will give zero mark corresponding to these assignments.

    Question 1:
    Find the first and second derivative of function f(x) at x=1.5 if:

    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

    MARKS 10

    Question 2:

    Using Newton’s forward interpolation formula, find the value of function f(1.6) if:

    x 1 1.4 1.8 2.2 f(x) 3.49 4.82 5.96 6.5

    MARKS 10

    MTH603 Assignment 2 Solution Spring 2021-converted.docx MTH603 Assignment 2 Solution Spring 2021.pdf

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    zaasmiZ

    @zaasmi said in MTH603 Grand Quiz Solution and Discussion:

    A series 16+8+4+2+1 is replaced by the series 16+8+4+2, then it is called

    Each number in the sequence is half the value of the number receding it. So the common difference in the series is dividing by two.

    16÷2=8

    8÷2=4

    4÷2=2

    2÷2=1

    1÷2=½

    The answer is ½ or 0.5

    When you keep dividing by two, you will notice an interesting pattern: the denominator continues to increase by two, while the numerator value remains the same. That’s fascinating because in natural, whole numbers the numbers in the series would decrease by two.

    1/4 , 1/8 , 1/16 etc.

  • decimal fractions

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    zaasmiZ

    @engr-ali said in decimal fractions:

    Assallamulikum Sir, Conversion (59)10 into binary 59/2=28-1 ? 28/2=14-0 14/2=7-0 7/2=3-1 3/2=1-1 (111001) ?

    Dear @Engr-Ali ,

    $(59){10} = (111011){2}$

    The mistake you have made is in the first step where you divided $59/2$. It has to be $29-1$ instead of $28-1$.

    Best wishes

  • Errors in Computations.

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    zaasmiZ

    @vu-kick said in Errors in Computations.:

    What is synchronous and asynchronous and what are there applications in real world. Which applications use this sort of techniques.

    The word synchronous and asynchronous are very general terms that are used in different fiels representing different phenonena. If you can please ask it more clearly that in what context you are asking. It will be good if you please mention what page of handouts, what slide of ppts or where in the lecture video of the numerical analysis you studied/heard about it. Then we’ll be able to explain it well.

    Best wishes

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    zaasmiZ

    @oxama-malik said in Solution of Non Linear Equations (Bisection Method):

    respected sir, sir ma na ye pochna tha ka regula falsi method ma hum ye bhi formula use kar sakta hai. please guide kar dya. the first approximation solution x1 is given by X1=(a(f(b))-b(f(a))/f(b)-f(a)

    That is right. You can use this formula.

    In fact, the formula given in the handouts becomes same after you simplify it. Also $x_{n-1}$ will become $a$ and $x_{n}$ will become $b$.

    So use any from the two formulas you find easier.

    Best wishes

  • replace the part of curve between the points

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    E

    @engr-ali said in replace the part of curve between the points:

    AoA, Sir if you may plz explain “replace the part of curve between the points A(x_n, f(x_n)) and B(x_n-1, f(x_n-1)) by a chord in the interval” . diagrammatic explanation will be a great help in comprehension of the subject matter. Thanks

    A chord is basically a straight line by joining two points of a curve or circle. The root of a equation means that when we give input value x then the functional value of that input will be zero then x is called the root of that equation. We take the two points of the interval on the chord instead of the curve shape because the value of root lies in that interval and this mean this value will lie on x-axis and if this is the root then functional value will be zero and we know that y-axis (functional value) is zero at x-axis.