IGNOU MPH 14 SOLVED ASSIGNMENT

Ques 1.

 Explain round-off error and truncation error, with one example of each.

Ques 2.

The series for e^x can be written as:

Calculate the truncation error when the first four terms of the series are used to evaluate e^1.5.

Ques 3.

Explain why a polynomial is a useful choice for an interpolating function. 

Ques 4.

 Use the Secant method with initial guesses of  and  to calculate the root/s of the equation  up to three iterations. Calculate the absolute relative approximate error at each stage.

Ques 5.

What are the advantages and drawbacks of the Secant method when compared to the Bisection Method and the Newton-Raphson Method? 

Ques 6.

 A population of single-celled organisms was grown in a Petri dish over a period of 24 hours. The number of organisms at a given time is recorded in the table below. Fit the data in the table below to an exponential model :

Ques 7.

Calculate the first derivative of the function  at  using the forward divided difference, backward divided difference and central divided difference methods with a step size of  rad. Also calculate the absolute true error in each case.

Ques 8.

Evaluate the integral  using the 2-point Gaussian Quadrature Rule with the following values:

Ques 9.

 Derive the Runge-Kutta 2nd Order formula for the differential equation

Ques 10.

Derive the Runge-Kutta 2nd Order formula for the differential equation

Use this to determine the value of y at  given that , using a step size .

Ques 11.

 Using the linear congruential random number generator determine the first five random numbers given that: , , , and . Transform these random numbers to lie between 0 and

Ques 12.

 What would be the maximum possible period of this random number sequence?

Ques 13.

Use the LU decomposition method to solve the following system of equations:

Ques 14.

 Explain round-off error and truncation error, with one example of each.

Ques 15.

The series for e^x can be written as:

Calculate the truncation error when the first four terms of the series are used to evaluate e^1.5.

Ques 16.

Explain why a polynomial is a useful choice for an interpolating function. 

Ques 17.

 Use the Secant method with initial guesses of  and  to calculate the root/s of the equation  up to three iterations. Calculate the absolute relative approximate error at each stage.

Ques 18.

What are the advantages and drawbacks of the Secant method when compared to the Bisection Method and the Newton-Raphson Method? 

Ques 19.

 A population of single-celled organisms was grown in a Petri dish over a period of 24 hours. The number of organisms at a given time is recorded in the table below. Fit the data in the table below to an exponential model :

Ques 20.

Calculate the first derivative of the function  at  using the forward divided difference, backward divided difference and central divided difference methods with a step size of  rad. Also calculate the absolute true error in each case.

Ques 21.

Evaluate the integral  using the 2-point Gaussian Quadrature Rule with the following values:

Ques 22.

 Derive the Runge-Kutta 2nd Order formula for the differential equation

Ques 23.

Derive the Runge-Kutta 2nd Order formula for the differential equation

Use this to determine the value of y at  given that , using a step size .

Ques 24.

 Using the linear congruential random number generator determine the first five random numbers given that: , , , and . Transform these random numbers to lie between 0 and

Ques 25.

 What would be the maximum possible period of this random number sequence?

Ques 26.

Use the LU decomposition method to solve the following system of equations:

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