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Produce a discrete time series
Produce a discrete time series y(t i ) by super positioning 5 cosinusoidal components, for your own choice of the amplitudes (a j ) and frequencies (f j

Calculate the cost of manufacturing
A manager has determined the cost C, in dollars, for manufacturing is C(q) =85log 10 (10+q/2) for manufacturing, where q is the number of units produced i

Calculate the heat transfer coefficient
A house wall may be approximated as two 1.2 cm layers of fiber insulating board, a 8 cm layer of loosely packed asbestos, and 10 cm layer of common brick. Assum

Partial differentiation
In estimating the cost of a pile of bricks measured as 2m*15m*1.2m,tape is stretched 1% beyond the standard length if the count is 450 bricks to 1m^3 and bricks

Laplace transformation
what are the uses of laplace transformation?

Simulating the second order system
First systems were described as systems that had one method of storing energy. Second order systems; wait for it.... have two methods of storing energy. Using

Find the polynomial
a) Use divided differences to ?nd the polynomial (in nested form) that interpolates the data b) Add the data point x = 6, y = 20 and hence estimate y f

Lagrangian coef?cient polynomials
Prove that the Lagrangian coef?cient polynomials for p n (x) satisfy ∑ n k=0 l k (x) = 1. Hint: It is only a 3line proof. Consider the interpolating poly

Linear programming
A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 ton

Value of real and imaginary parts
In the x,y plane, divide up the xaxis by placing marks at x=a, x=b, and x = 2. Suppose φ is harmonic in the upper half plane and on the segments of the xaxis

Draw concentric circles
Draw concentric circles of radii a and b, each centered at z=id (on the imaginary axis). Suppose φ(x,y) is a harmonic function inside the washer defined by thes

Substitution method
Answer the following set of simultaneous equations using elimination or substitution method. a) xy +z= 10 b) 3x+y+2z=34 c) 5x+2yz=14

Jacobian
if u=x^22y^2, v=2x^2y^2 and x=rcosp ad y=rsinp, find the value of the jacobian d(u,v)/d(r,p)

Dynamics
The acceleration of an oscillating particle is defined by the relation a = kx Determine the value of k such that v = 15 in./s when x = 0 and x = 3 in. and v =

Find the variance and covariance
The following are 8 data points that shows the relationship between the number of fishermen and the amount of fish they can catch a day. (Let the number of fish

