<?xml version="1.0" encoding="UTF-8"?><rss xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:atom="http://www.w3.org/2005/Atom" version="2.0"><channel><title><![CDATA[Topics tagged with mth603]]></title><description><![CDATA[A list of topics that have been tagged with mth603]]></description><link>https://community.secnto.com//tags/mth603</link><generator>RSS for Node</generator><lastBuildDate>Mon, 08 Jun 2026 19:23:40 GMT</lastBuildDate><atom:link href="https://community.secnto.com//tags/mth603.rss" rel="self" type="application/rss+xml"/><pubDate>Invalid Date</pubDate><ttl>60</ttl><item><title><![CDATA[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]]></title><description><![CDATA[@zaasmi said in 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:

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

In double integration, the interval [a, b] ￼ is typically divided into equal subintervals of size k, and the interval [c, d] ￼ is divided into equal subintervals of size h￼.
So, the correct answer is equal, equal.
This means both intervals are subdivided into equal lengths, making it easier to apply numerical methods like the rectangle method, trapezoidal rule, or Simpson’s rule in double integration.
]]></description><link>https://community.secnto.com//topic/2670/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</link><guid isPermaLink="true">https://community.secnto.com//topic/2670/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</guid><dc:creator><![CDATA[zaasmi]]></dc:creator><pubDate>Invalid Date</pubDate></item><item><title><![CDATA[The (n + 1) th difference of a polynomial of degree n is...]]></title><description><![CDATA[@zaasmi said in The (n + 1) th difference of a polynomial of degree n is...:

The (n + 1) th difference of a polynomial of degree n is…
Answer
0
Constant
n +1

The (n + 1) difference of a polynomial of degree n is 0.
This is because the differences eventually reach a constant value after taking differences equal to the degree of the polynomial plus one. Therefore, for a polynomial of degree n ￼, the (n + 1) difference will always be zero.
Thus, the correct answer is 0.
]]></description><link>https://community.secnto.com//topic/2669/the-n-1-th-difference-of-a-polynomial-of-degree-n-is</link><guid isPermaLink="true">https://community.secnto.com//topic/2669/the-n-1-th-difference-of-a-polynomial-of-degree-n-is</guid><dc:creator><![CDATA[zareen]]></dc:creator><pubDate>Invalid Date</pubDate></item><item><title><![CDATA[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]]></title><description><![CDATA[@zaasmi said in 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:

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

In the context of backward difference, the relationship between the step size  h  ￼ and the point  P￼ can be expressed as:
x - x_n = Ph
￼
Thus, the correct answer is x - x_n = Ph.
This expression indicates that the difference between a point ￼ and a previous point  x_n  ￼ can be represented as a multiple of the step size  h  ￼.
]]></description><link>https://community.secnto.com//topic/2668/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</link><guid isPermaLink="true">https://community.secnto.com//topic/2668/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</guid><dc:creator><![CDATA[zaasmi]]></dc:creator><pubDate>Invalid Date</pubDate></item><item><title><![CDATA[In integrating $&#x5C;int_{0}^{&#x5C;frac{2}{2}} &#x5C;cos x d x$ by dividing the interval into four equal parts, width of the interval should be]]></title><description><![CDATA[@zaasmi said in 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:

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
$\frac{\pi}{2}$
$\pi$
$\frac{\pi}{8}$

To determine the width of each interval for the integral \int_{0}^{\frac{\pi}{2}} \cos x , dx  ￼ by dividing the interval into four equal parts, we use the formula:
h = \frac{b - a}{n}
where:
•	a = 0,
•	b = \frac{\pi}{2},
•	n = 4.

Calculating h:
h = \frac{\frac{\pi}{2} - 0}{4} = \frac{\frac{\pi}{2}}{4} = \frac{\pi}{8}
So, the width of the interval should be \frac{\pi}{8} ￼.
Thus, the correct answer is \frac{\pi}{8} ￼.
]]></description><link>https://community.secnto.com//topic/2667/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</link><guid isPermaLink="true">https://community.secnto.com//topic/2667/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</guid><dc:creator><![CDATA[zaasmi]]></dc:creator><pubDate>Invalid Date</pubDate></item><item><title><![CDATA[In fourth order Runge-Kutta method K 4]]></title><description><![CDATA[@zaasmi said in In fourth order Runge-Kutta method K 4:

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)

In the fourth-order Runge-Kutta method,  k_4 , ￼ is given by the formula:
k_4 = h \cdot f\left(x_n + h, y_n + k_3\right)
￼
However, from the options you’ve provided, it seems that none of them correctly represent the standard formulation for  k_4  ￼.
To clarify based on standard notation:
•	￼  k_4  depends  on the function evaluated at the next step after adding the entire step size  h  to  x_n  and the third slope  k_3  to  y_n .

If the options don’t include the correct form for  k_4 ￼, then the answer would be None of the given choices.
]]></description><link>https://community.secnto.com//topic/2666/in-fourth-order-runge-kutta-method-k-4</link><guid isPermaLink="true">https://community.secnto.com//topic/2666/in-fourth-order-runge-kutta-method-k-4</guid><dc:creator><![CDATA[zaasmi]]></dc:creator><pubDate>Invalid Date</pubDate></item><item><title><![CDATA[In fourth order Runge-Kutta method k2]]></title><description><![CDATA[@zaasmi said in In fourth order Runge-Kutta method k2:

In fourth order Runge-Kutta method k2
is given by
Answer
^2-“/”“” З’Уп 3’
k2 = 45(-12.30-42)

In the fourth-order Runge-Kutta method, ￼ is computed using the following formula:
￼
k_2 = h \cdot f\left( t_n + \frac{h}{2}, y_n + \frac{k_1}{2} \right)
where:
•	￼  h  is the step size
•	￼  t_n  is the current value of the
•	￼  y_n  is the current value of the dependent variable,
•	￼  k_1 = h \cdot f(t_n, y_n)  is the first slope.

The formula you provided seems to be incorrect or misformatted. If you have specific terms or a function f(t, y) ￼, please clarify or correct the notation so I can provide the accurate calculation for ￼ in your context.
]]></description><link>https://community.secnto.com//topic/2665/in-fourth-order-runge-kutta-method-k2</link><guid isPermaLink="true">https://community.secnto.com//topic/2665/in-fourth-order-runge-kutta-method-k2</guid><dc:creator><![CDATA[zaasmi]]></dc:creator><pubDate>Invalid Date</pubDate></item><item><title><![CDATA[What is the Process of finding the values outside the interval (Xo,x,) called?]]></title><description><![CDATA[@zaasmi said in What is the Process of finding the values outside the interval (Xo,x,) called?:

What is the Process of finding the values outside the interval (Xo,x,) called?
Answer
interpolation
iteration
Polynomial equation
extrapolation

The process of finding the values outside the interval ￼ is called extrapolation.
So, the correct answer is extrapolation.
Extrapolation involves estimating values beyond the known data points, while interpolation estimates values within the range of known data.
]]></description><link>https://community.secnto.com//topic/2664/what-is-the-process-of-finding-the-values-outside-the-interval-xo-x-called</link><guid isPermaLink="true">https://community.secnto.com//topic/2664/what-is-the-process-of-finding-the-values-outside-the-interval-xo-x-called</guid><dc:creator><![CDATA[zaasmi]]></dc:creator><pubDate>Invalid Date</pubDate></item><item><title><![CDATA[When we apply Simpson&#x27;s 3&#x2F;8 rule, the number of intervals n must be]]></title><description><![CDATA[@zaasmi said in When we apply Simpson's 3/8 rule, the number of intervals n must be:

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

When applying Simpson’s 3/8 rule, the number of intervals ￼ must be a multiple of 3.
Thus, the correct answer is Multiple of 3.
This requirement ensures that each set of three intervals can be used to apply the 3/8 rule effectively.
]]></description><link>https://community.secnto.com//topic/2663/when-we-apply-simpson-s-3-8-rule-the-number-of-intervals-n-must-be</link><guid isPermaLink="true">https://community.secnto.com//topic/2663/when-we-apply-simpson-s-3-8-rule-the-number-of-intervals-n-must-be</guid><dc:creator><![CDATA[zaasmi]]></dc:creator><pubDate>Invalid Date</pubDate></item><item><title><![CDATA[Milne&#x27;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.]]></title><description><![CDATA[@zaasmi said in 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.:

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

Milne’s predictor-corrector (P-C) method is a multi-step method where we assume that the solution to the given initial value problem is known at past 3 equally spaced points.
Thus, the correct answer is 3.
Milne’s method uses information from three previous points to predict the next value, making it a third-order method in terms of accuracy.
]]></description><link>https://community.secnto.com//topic/2662/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</link><guid isPermaLink="true">https://community.secnto.com//topic/2662/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</guid><dc:creator><![CDATA[zaasmi]]></dc:creator><pubDate>Invalid Date</pubDate></item><item><title><![CDATA[The truncation error in Adam&#x27;s predictor formula is ....-times more than that in corrector formula]]></title><description><![CDATA[@zaasmi said in The truncation error in Adam's predictor formula is ....-times more than that in corrector formula:

The truncation error in Adam’s predictor formula is …-times more than that in corrector formula
Answer
10
11
12
13

The truncation error in Adam’s predictor formula is typically 12 times more than that in the corrector formula.
Thus, the correct answer is 12.
Adam’s predictor-corrector methods involve using an explicit predictor to estimate the next value and then refining it with an implicit corrector. The predictor has a higher truncation error compared to the corrector.
]]></description><link>https://community.secnto.com//topic/2661/the-truncation-error-in-adam-s-predictor-formula-is-times-more-than-that-in-corrector-formula</link><guid isPermaLink="true">https://community.secnto.com//topic/2661/the-truncation-error-in-adam-s-predictor-formula-is-times-more-than-that-in-corrector-formula</guid><dc:creator><![CDATA[zaasmi]]></dc:creator><pubDate>Invalid Date</pubDate></item><item><title><![CDATA[To apply Simpson&#x27;s 3&#x2F;8 rule, the number of intervals be]]></title><description><![CDATA[@zaasmi said in To apply Simpson's 3/8 rule, the number of intervals be:

Answer
10
11
12
13

To apply Simpson’s 3/8 rule, the number of intervals must be a multiple of 3.
Among the given options, the correct choice is 12, as it is divisible by 3. This rule approximates the integral using cubic polynomials over sets of three intervals, so the total number of intervals should be a multiple of 3 for the rule to apply.
]]></description><link>https://community.secnto.com//topic/2660/to-apply-simpson-s-3-8-rule-the-number-of-intervals-be</link><guid isPermaLink="true">https://community.secnto.com//topic/2660/to-apply-simpson-s-3-8-rule-the-number-of-intervals-be</guid><dc:creator><![CDATA[zaasmi]]></dc:creator><pubDate>Invalid Date</pubDate></item><item><title><![CDATA[Which formula is useful in finding the interpolating polynomial?]]></title><description><![CDATA[@zaasmi said in Which formula is useful in finding the interpolating polynomial?:

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

The correct answer is Lagrange’s interpolation formula.
Since the data points ￼ = {1, 2, 5, 9} are unequally spaced, Lagrange’s interpolation formula is the appropriate method to find the interpolating polynomial. Newton’s forward and backward difference interpolation formulas are typically used when the data points are equally spaced, which is not the case here.
Therefore, Lagrange’s interpolation is best suited for this dataset.
]]></description><link>https://community.secnto.com//topic/2659/which-formula-is-useful-in-finding-the-interpolating-polynomial</link><guid isPermaLink="true">https://community.secnto.com//topic/2659/which-formula-is-useful-in-finding-the-interpolating-polynomial</guid><dc:creator><![CDATA[zaasmi]]></dc:creator><pubDate>Invalid Date</pubDate></item><item><title><![CDATA[MTH603 Assignment 1 Solution and Discussion]]></title><description><![CDATA[@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

]]></description><link>https://community.secnto.com//topic/2326/mth603-assignment-1-solution-and-discussion</link><guid isPermaLink="true">https://community.secnto.com//topic/2326/mth603-assignment-1-solution-and-discussion</guid><dc:creator><![CDATA[zaasmi]]></dc:creator><pubDate>Invalid Date</pubDate></item><item><title><![CDATA[mth603 final term solved papers by moaaz]]></title><description><![CDATA[@zaasmi said in mth603 final term solved papers by moaaz:

@zaasmi said in mth603 final term solved papers by moaaz:

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]]></description><link>https://community.secnto.com//topic/2311/mth603-final-term-solved-papers-by-moaaz</link><guid isPermaLink="true">https://community.secnto.com//topic/2311/mth603-final-term-solved-papers-by-moaaz</guid><dc:creator><![CDATA[zaasmi]]></dc:creator><pubDate>Invalid Date</pubDate></item><item><title><![CDATA[MTH603 Download Handout]]></title><description><![CDATA[Download MTH603 Handout
]]></description><link>https://community.secnto.com//topic/2263/mth603-download-handout</link><guid isPermaLink="true">https://community.secnto.com//topic/2263/mth603-download-handout</guid><dc:creator><![CDATA[zaasmi]]></dc:creator><pubDate>Invalid Date</pubDate></item><item><title><![CDATA[MTH603 Assignment 1 Solution and Discussion]]></title><description><![CDATA[@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
[center][image: wNTUZAq.png][/center]
]]></description><link>https://community.secnto.com//topic/2223/mth603-assignment-1-solution-and-discussion</link><guid isPermaLink="true">https://community.secnto.com//topic/2223/mth603-assignment-1-solution-and-discussion</guid><dc:creator><![CDATA[cyberian]]></dc:creator><pubDate>Invalid Date</pubDate></item></channel></rss>