SE301: Introduction to Numerical Methods Summer 033 Sections 5 and 6 Computer Assignment
Instructor: Dr. Samir AlAmer
General Instructions:
2: The program is wellwritten and the results are correct 1: A series attempt to solve the problem was done but the program is not complete or the answer is not correct. 0: The assignment was not submitted or submitted too late or no series attempt to solve the problem was done.
Computer Assignment # 1 Due to :_____________
The N^{th} order Taylor series expansion of f(x) = sin(x) is given by Write a program that computes sin(0.2) using N = 1, 2, 3, 4 and 5. Compute and print the percentage relative error
Use the builtin sine function to evaluate the true value. Display the result in a tabulated form.
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Computer Assignment # 2 Due to :_____________
The volume V of a liquid in a spherical tank of radius r is related to the depth h of the liquid is given by . Given h = 1m and V = 0.5m^{3} Assuming the initial interval [0,2], Write a program that uses Bisection method to determine h with fourdecimaldigit accuracy. Your program should display the estimated level. ______________________________________________________________________________
Computer Assignment # 3 Due to :_____________
The trajectory of a ball thrown by a player is defined in terms of its (x,y)coordinates. The trajectory is modeled by where g = 9.81 and . Write a program that implements the Secant method to determine the initial angle with fourdecimaldigit accuracy so that the ball hit a target with coordinate (40,1). Use 30 and 40 degrees as initial guesses.
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Computer Assignment # 4 Due to :_____________
The nodevoltage law was applied to an electrical circuit and the following equations were obtained.
Write a program that implements the Naive Gaussian elimination and use it to solve for the unknowns V_{1}, V_{2} and V_{3} and display their values.
Computer Assignment # 5 Due to :_____________
The upward velocity of a rocket can be computed as where u : velocity at which burned fuel exit the rocket (u = 2000m/s) : initial mass of the rocket (= 150000 kg) q : fuel consumption rate (q = 2600 kg/s) g : gravitational constant (g = 9.81) t : time
Write a program that implements the Romberg method of order O(h^{8}) to compute the height the rocket reaches after 30 seconds. Your program should display the Romberg table.
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Computer Assignment # 6 Due to :_____________
A mathematical model for the area A (in cm^{2}) that a colony of bacteria occupies is given by
Write a program that uses the Fourth order RungeKutta method to compute the area over the interval [0, 5]. Assume the initial area is 0.2 cm^{2} and use h = 0.05. Your program should display the area after 5 time units and a graph to show the area during the studied interval is also needed.
