# MTH603 Assignment 2 Solution and Discussion

• Assignment NO. 2 MTH603 (Fall 2020)

Maximum Marks: 20
Due Date: February 15, 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 - 35 lectures.
Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in the 23-35lectures.
• Upload assignments properly through LMS, No Assignment will be accepted through email.
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 44

Hence find y(3). MARKS 10

• 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.
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 2.5 3 3.5 4 f(x) 3.375 7 13.625 24 38.875 59

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

• 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.
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 2.5 3 3.5 4 f(x) 3.375 7 13.625 24 38.875 59

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

• 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.
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 2.5 3 3.5 4 f(x) 3.375 7 13.625 24 38.875 59

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

• Question 1:
Obtain the value of using Simpson’s 1/3 rule correct to 3 decimal places.
MARKS 10

Solution Idea.

We evaluate the given integral by the formula

S4=Δx3[f(x0)+4f(x1)+2f(x2)+4f(x3)+2(x4)].

Determine the width of the subinterval:

Δx=b−an=1−04=14.

Compute the function values at the endpoints of the subintervals:

f(x0)=f(0)=e0=1;

f(x1)=f(14)=e14=4√e≈1.2840;

f(x2)=f(12)=e12=√e≈1.6487;

f(x3)=f(34)=e34=4√e3≈2.1170;

f(x4)=f(1)=e1=e≈2.7183;

Plugging in the function values into our equation, we get:

1∫0exdx≈S4=112[1+4×1.2840+2×1.6487+4×2.1170+2.7183]=112×20.6197=1.7183≈1.718  1

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• ## Solution of Non Linear Equations (Bisection Method) MTH603 - Numerical Analysis • non linear equations bisection method • • Oxama Malik

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