New PDF release: Engineering Analysis: Interactive Methods and Programs with

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Extra info for Engineering Analysis: Interactive Methods and Programs with FORTRAN, QuickBASIC, MATLAB, and Mathematica

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R Out[9] = {5, 4} The solution of x1 = 5 and x2 = 4 do satisfy the equations x1 + 2x2 = 13 and 3x1 + 4x2 = 31. TRANSFORMATION OF COORDINATE SYSTEMS, ROTATION, AND ANIMATION Matrix algebra can be effectively applied for transformation of coordinate systems. When the cartesian coordinate system, x-y-z, is rotated by an angle ⍜z about the z-axis to arrive at the system xЈ-yЈ-zЈ as shown in Figure 2, where z and zЈ axes coincide and directed outward normal to the plane of paper, the new coordinates of a typical point P whose coordinates are (xP,yP,zP) can be easily obtained as follows: x ′P = OP cos(θ P − θ z ) = (OP cos θ P ) cos θ z + (OP sin θ P ) sin θ z = x P cos θ z + y p sin θ z y ′P = OP sin(θ P − θ z ) = (OP sin θ P ) cos θ z − (OP cos θ P ) sin θ z = x p sin θ z + y p sin θ z © 2001 by CRC Press LLC 4.

7. Repeat Problem 6 but use MATLAB. 8. 5 Use indicial notation to express the above two equations and then develop a subroutine meanSD(X,N,RM,SD) for taking the N values of X to compute the real value of mean, RM, and standard deviation, SD. 9. 001% of the partial sum of series in magnitude: Sin x = x1 x3 x 5 − + −… 1! 3! 5! Notice that Sin(x) is an odd function so the series contains only terms of odd powers of x and the series carries alternating signs. Compare the result of the program SinePgrm with those obtained by application of the library function Sin available in FORTRAN and QuickBASIC.

Also, Mathematica has a function called Transpose for transposition of a matrix. 3 SOLUTION OF MATRIX EQUATION Matrix notation offers the convenience of organizing mathematical expression in an orderly manner and in a form which can be directly followed in coding it into programming languages, particularly in the case of repetitive computation involving the looping process. The most notable situation is in the case of solving a system of linear algebraic equation. For example, if we need to determine a linear equation y = a1 + a2x which geometrically represents a straight line and it is required to pass through two specified points (x1,y1) and (x2,y2).

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