

Re: MTH603 Assignment 2 Solution and Discussion
Assignment NO. 2 MTH603 (Fall 2020)
Maximum Marks: 20
Due Date: February 15, 2021DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
• To solve this assignment, you should have good command over 23  35 lectures.
Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in the 2335lectures.
• 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:
Obtain the value of using Simpson’s 1/3 rule correct to 3 decimal places.
MARKS 10
Question 2:Using Newton’s divided difference formula, find the quadratic equation for the following data:
X 1 2 5
Y 8 14 44Hence find y(3). MARKS 10



Re: MTH603 Assignment 1 Solution and Discussion
Question #1: Find the root of the equation x^3+x^2+x1 =0 correct to two decimal places by using bisection method.
Question #2: Solve the system of linear equations with the help of Gaussian elimination method.
2x + y + z = 9;3x −2y + 4z = 9;x +y2z = 3Solution File

Question 1:
Convert the decimal number 80 into its binary equivalent.
Question 2:
Convert the binary number 2 (11001100) to its decimal equivalent.
Question 3:
Find the relative error when 17 is considered upto four decimal places.
Question 4:
Find the interval in which atleast one root of the equation 3 2 xx x 2 10 lies.
Question 5:
Find the real root of the equation 4 x x 10 0 in the interval [1, 2] by bisection method upto
two iterations. 
MTH603_Final_Term_(GIGA_FILE_by_Ishfaq_V11.02.02).pdf
MTH603 Spring_2010_FinalTerm_OPKST_.doc
MTH603 solvedbyAtifAli…doc
MTH603 finalterm paper 2.doc
MTH603 finalterm paper 1.doc
MTH603 final.pdf MTH603 Final.doc MTH603  Final Term Papers.pdf
MTH603  Final Term Papers 02.pdf
MTH603 Final term papers in one file.pdf 
Assignment NO. 2 MTH603 (Spring 2020)
Maximum Marks: 20 Due Date: August 13, 2020
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 2330 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 that if 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 :
Using difference operator formulas (Δ and ∇) and the values given in the table below,
x 0.3 0.5 0.7 0.9 1.1 1.3
y 3.9118 3.8234 3.6773 3.4807 3.2408 2.9648estimate the value of
y^' (0.3) Marks 10 y''(1.3) Marks 10 
Grand Quiz Total Questions : 30
Please read the following instructions carefully!
Quiz will be based upon Multiple Choice Questions (MCQs).You have to attempt the quiz online. You can start attempting the quiz any time within given date(s) of a particular subject by clicking the link for Quiz in VULMS.
Each question has a fixed time of 90 seconds. So you have to save your answer before 90 seconds. But due to unstable internet speeds, it is recommended that you should save your answer within 60 seconds. While attempting a question, keep an eye on the remaining time.
Attempting quiz is unidirectional. Once you move forward to the next question, you can not go back to the previous one. Therefore before moving to the next question, make sure that you have selected the best option.
DO NOT press Back Button / Backspace Button while attempting a question, otherwise you will lose that question.
DO NOT refresh the page unnecessarily, specially when following messages appear
Saving…
Question Timeout: Now loading next question…Javascript MUST be enabled in your browser; otherwise you will not be able to attempt the quiz.
If for any reason, you lose access to internet (like power failure or disconnection of internet), you will be able to attempt the quiz again from the question next to the last shown question. But remember that you have to complete the quiz before expiry of the deadline.
If any student failed to attempt the quiz in given time then no retake or offline quiz will be held.
Start Quiz

Re: MTH603 Assignment 1 Solution and Discussion
Question 1: Find the root of on equation f(x) =2coshx sinx1 taking initial value x0 = 0.4, using Newton Raphson Method. Convert Up to four decimal places.
Question 2: Evaluate √167 by Newton Raphson Method correct up to 4 decimal places.

Assignment NO. 1 MTH603 (Fall 2019)
Maximum Marks: 20 Due Date: 24 112019
DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
• To solve this assignment, you should have good command over 01  12 lectures.
• Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in the 01 to 12 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 that if 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 root of the equation, Perform three iteration of the equation,
ln (x −1) + sinx = 0 by using Newton Raphson method.
Question #2: Solve the system of linear equations with the help of Gaussian elimination method.
x + y + z = 6; 2x − y + z = 3; x + z = 4
MTH603 Grand Quiz Solution and Discussion

Grand Quiz Total Questions : 30
Please read the following instructions carefully!
Quiz will be based upon Multiple Choice Questions (MCQs).You have to attempt the quiz online. You can start attempting the quiz any time within given date(s) of a particular subject by clicking the link for Quiz in VULMS.
Each question has a fixed time of 90 seconds. So you have to save your answer before 90 seconds. But due to unstable internet speeds, it is recommended that you should save your answer within 60 seconds. While attempting a question, keep an eye on the remaining time.
Attempting quiz is unidirectional. Once you move forward to the next question, you can not go back to the previous one. Therefore before moving to the next question, make sure that you have selected the best option.
DO NOT press Back Button / Backspace Button while attempting a question, otherwise you will lose that question.
DO NOT refresh the page unnecessarily, specially when following messages appear
Saving…
Question Timeout: Now loading next question…Javascript MUST be enabled in your browser; otherwise you will not be able to attempt the quiz.
If for any reason, you lose access to internet (like power failure or disconnection of internet), you will be able to attempt the quiz again from the question next to the last shown question. But remember that you have to complete the quiz before expiry of the deadline.
If any student failed to attempt the quiz in given time then no retake or offline quiz will be held.
Start Quiz


Let[A]bea3×3realsymmetricmatrixwitha23bethenumericallylargestoff−diagonalelementthenusingJacobi′smethodthevalueofθcanbefoundby
Let A be a 3×3 matrix with real entries. Prove that if A is not similar over
R to a triangular matrix then A is similar over C to a diagonal matrix. 
While using Relaxation method, which of the following is increment ‘dxi’corresponding to the largest Residual for 1st iteration on the system;
2x+3y = 1, 3x +2y =  4 ? 
Central Difference method is the finite difference method
Finite difference. A finite difference is a mathematical expression of the form f (x + b) − f (x + a). … The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems.


Whileusingtherelaxationmethodforfindingthesolutionofthefollowingsystem11x1+x2−x3=8 x1+8x2+5x3=9 x1+x2+9x3=7withtheinitialvector(0,0,0),theresidualswouldbe

By using determinants, we can easily check that the solution of the given system of linear equation ______ and it is ______.

If the determinant of a matrix A is not equal to zero then the system of equations will have……….
A nxn nonhomogeneous system of linear equations has a unique nontrivial solution if and only if its determinant is nonzero. If this determinant is zero, then the system has either no nontrivial solutions or an infinite number of solutions.

For the system of equations; x =2, y=3. The inverse of the matrix associated with its coefficients is.

While using Jacobi method for the matrix
A=⎡⎣⎢⎢11/41/21/41/31/41/21/41/5⎤⎦⎥⎥the value of ‘theta θ’ can be found as

If the Relaxation method is applied on the system; 2x+3y = 1, 3x +2y =  4, then largest residual in 1st iteration will reduce to .

Whichofthefollowingisaforwarddifferencetableforthegivenvaluesofxandy?xy0.10.0030.50.1480.90.37

While using Relaxation method, which of the following is the largest Residual for 1st iteration on the system;
2x+3y = 1, 3x +2y =  4 ? 
Let [A] be a 3x3 real symmetric matrix with
a12
be numerically the largest offdiagonal element of A, then we can construct orthogonal matrix S1 by Jacobi’s method as 
The number of significant digits in the number 608.030060 is:
9