66665 – Department of Mathematics and Philosophy of EngineeringMHZ3531

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Department of Mathematics and Philosophy of EngineeringMHZ3531 Engineering Mathematics IAAssignment No: 2Academic Year: 2020/2021 Due Date: Will be notify laterInstructions• Answer all the questions.• Attach the cover page with your answer scripts.• Use both sides of papers when you are answering the assignment.• Please send the answer scripts of your assignment on or before the due date to the following address.Course Coordinator – MHZ3531,Dept. of Mathematics & Philosophy of Engineering,Faculty of Engineering Technology,The Open University of Sri Lanka,P.O. Box 21,Nawala,Nugegoda.MHZ3531-Engineering Mathematics IAAssignment 2Q1 (a) Write down the order and the degree of the following differential equations.i) ???? ???? + (???? + sin ??) = 0 ii) ??2?? 3 ???? 4 3iii) ??3?? 5 ??2?? iv) ??2?? 3v)(b) Using the method of variable separation, solve the following differential equationsi) (???? + ??)???? = (??2??2 + ??2+??2 + 1)????ii)iii)iv) ??????2?? ???? = ??????2?? ????v)Q2 (a) Solve the following homogeneous differential equations.i) ???? ???? ii)iii) ???? iv)b) Show that the following differential equations are exact and solve them.i)ii) (?? + sin ??)???? + (?? cos ?? – 2??)???? = 0 iii) 2?? + ?? cos ????)???? + ?? cos ???? ???? = 0(c) Using an integrating factor, solve the following differential equations.i) (??2 + ??2 + ??)???? + ???? ???? = 0ii).Q3?? = ??????, then show that ?? has two distinct real values. Further, if the values of ?? are ??1 and ??2, then show that ?? = ??1????1?? + ??2????2?? is the complete primitive of the given differential equation, where ??1 and ??2 are arbitrary constants.?? = ??????, then show that ?? has two distinct imaginary values. Further, show that the complete primitive of the above differential can be expressed of the form?? = ??????(??1 cos ???? + ??2 sin ????), where ??1 and ??2 are arbitrary constants.Q4 (a) Let ??(??) = ??2 – 3. Show that the equation ??(??) = 0 has a root between 1 and 2.i) By using the bisection method, find a solution for the above equation correct to nine decimal places.ii) By applying Newton Raphson’s method, find a solution for above equation correct to nine decimal places taking ??0 = 1.5.(b) Using Newton’s interpolation divided difference formula and the following table calculate an approximation value for ??(1.5).???? -2 0 1 4 5??(????) -8 0 1 64 125(c) Using Lagrange’s interpolation formula and the following table, calculate an approximation value for ??(10).???? 5 6 9 11??(????) 12 13 14 16where ?? interpolates ?? at these points.Q5 (a) Write down Trapezoidal Rule and Simpson’s rule to approximate the finite.i) Using the Trapezoidal Rule with ?? = 6 subintervals, approximate the integralapproximation.ii) Using Simpson’s Rule with ?? = 4 subintervals, approximate theintegral ? ?? ?? ???? to 3 decimal places. Estimate the relative percent-2error of the approximation.(b) Using the Jacobi’s iteration method, find the sixth iteration of the solution of the following system of equations.3?? + 10?? – ?? = -82?? – 3?? + 10?? = 1510?? + ?? – 2?? = 7End-Copyrights Reserved-

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