

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 = 3 
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. 
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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
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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 Quiz 1 Solution and Discussion

@zareen said in MTH603 Quiz 1 Solution and Discussion:
Interpolation
Reff
In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing new data points within the range of a discrete set of known data points. 
@zareen said in MTH603 Quiz 1 Solution and Discussion:
Extrapolation
In mathematics, extrapolation is a type of estimation, beyond the original observation range, the value of a variable on the basis of its relationship with another …

@zareen said in MTH603 Quiz 1 Solution and Discussion:
In Simpson’s 1/3 rule, the global error is of ……………… MTH603
Mth603 Just Final term MCQS (latest quiz included and FAQs and Glossary is also included in this file) Plz. … This preview shows page 1  3 out of 46 pages. … True False In Simpson’s 3/8 rule, the global error is of O(h2) O(h3) O(h4) None of …

@zareen said in MTH603 Quiz 3 Solution and Discussion:
δ = E 1/2  E 1/2
δ δ. + terms involving high powers of δx1, δx2 are infinitesimal their squares and higher powers … [eh  1] ∆ex = (eh – 1)( e(x+h)  ex ) = (eh – 1)2 ex. ∴∆2 eax …
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@zareen said in MTH603 Quiz 1 Solution and Discussion:
Please share your Quiz
Choose your region. Enter your name. Answer 10 Questions about yourself. Your quiz link will be created. Share your quiz link with your friends. Your friends will …

@zareen said in MTH603 Quiz 1 Solution and Discussion:
Y’=(x)=1+Some truncation Error
EXAMPLE 1 Bound for Local Truncation Error Find a bound for the local … the local truncation error for any of the five steps given in Table 6.1.1 by replacing c by …
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@zareen said in MTH603 Quiz 1 Solution and Discussion:
For a function ‘f(x) = x’, with a step size of ‘h=0.01’, which of the following gives the 1st derivative at x =1 by using two point formula? MTH603
approximate the function f (x) = cos x by the series. 2. 4. 2 … An equation f(x)=0 is said to be the algebraic equation in x if it is purely a … between these two points and therefore, a root lies between these two points.

@zareen said in MTH603 Quiz 1 Solution and Discussion:
(y2 + y4)/2
IR Row Orbital Symmetry function Bonding a1 s(M) s( M) Sigma s(L) (s1 +s2+s3+s4)/2 p(L) (x1+y1+z1−x2− y2+z2−x3+y3 −z3 +x4− y4−z4)/ √ 12 e 1 d(M) dx2 (M)

@zareen said in MTH603 Quiz 1 Solution and Discussion:
While using the Composite Trapezoidal form for integrating y = f(x) in [0,10] which is subdivided in equally spaced interval of width ‘h =2’, then which of the following is the area of associated trapezoidal strip over subinterval:[2,4] ? MTH603
In mathematics, and more specifically in numerical analysis, the trapezoidal rule is a technique … The trapezoidal rule works by approximating the region under the graph of the … {\displaystyle {d^{2}g_{k} \ over dt.

@zareen said in MTH603 Quiz 1 Solution and Discussion:
Polynomial Function
In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and nonnegative integer exponents of variables. An example of a polynomial of a single indeterminate, x, is x² − 4x + 7
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@zareen said in MTH603 Quiz 1 Solution and Discussion:
Logarithmic Function
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.
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@zareen said in MTH603 Quiz 1 Solution and Discussion:
Exponential Function
In mathematics, an exponential function is a function of the form. where b is a positive real number, and in which the argument x occurs as an exponent. For real numbers c and d, a function of the form is also an exponential function, as it can be rewritten as.

@zareen said in MTH603 Quiz 1 Solution and Discussion:
Trigonometric Function
In mathematics, the trigonometric functions are real functions which relate an angle of a rightangled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

@zareen said in MTH603 Quiz 1 Solution and Discussion:
In NewtonCotes formula for finding the definite integral of a tabular function, which of the following is taken as an approximate function then find the desired integral? MTH603
In numerical analysis, Simpson’s method is a method for numerical integration, the numerical approximation of definite integrals. … Simpson’s rule also corresponds to the threepoint NewtonCotes quadrature rule

@zareen said in MTH603 Quiz 1 Solution and Discussion:
Series acceleration method
In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series. Techniques for series acceleration are often applied in numerical analysis, where they are used to improve the speed of numerical integration.
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@zareen said in MTH603 Quiz 1 Solution and Discussion:
Sequence acceleration method
In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series. Techniques for series acceleration are often applied in numerical analysis, where they are used to improve the speed of numerical integration.