Reference no: EM132590332
Engineering Mathematics Questions -
Q1. For the following data set:
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xj
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f(xi)
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First
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Second
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Third
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0.1*C
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e0.1*C
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0.2*C
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e0.2*C
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0.3*C
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e0.3*C
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0.4*C
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e0.4*C
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where, C = last non-zero digit of your student ID .
a) Complete the divided difference chart.
b) Use the information above to approximate f(0.12*C) using a quadratic Newton interpolating function.
c) Use the information in (a) and (b) above to approximate f(0.12*C) using a cubic Newton interpolating function.
Q2. For y' = (y - t - 1)2 + 2 and y(0) = 1
a) Use the Euler method to integrate from t = 0 to 0.09*C with h = 0.03*C. Where, C = last non-zero digit of your student ID.
b) Use the 4th order Runge-Kutta method to numerically integrate the equation above for t = 0 to 0.03*C with h = 0.03*C and y(0) = 1.
Q3. For f(x) = x2e-x and h = 0.05*C, where, C = last non-zero digit of your student ID
a) Use forward and backward approximations to estimate the first derivative of f(x) at x = 1.2. Use the most accurate formulas available.
b) Using the least accurate centered difference formulas, estimate the first and second derivatives of f(x) at x= 1.2.
Q4. For I = 0∫1.2*C√(1+x2)dx, where, C = last non-zero digit of your student ID
a) Evaluate I using the trapezoidal rule with n = 4.
b) Evaluate I using the 1/3 Simpson's rule with n = 2.