By T.T. Furman (Eds.)
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9). B. Due to symmetry points in one quadrant only need to be dealt with. Case A 16 square grid, h, and since we have for point (1) and since = $a. 21) we get for point (0) 28 APPROXIMATE METHODS IN ENGINEERING DESIGN 1. 375h; GO 4% = 0 (for a 16 square matrix) (Aiv) Case B 36 square matrix h, = 4 6 . 1925 2 . . e. 7% higher. 2. Approximate computations. 3. Relationships between trigonometric and exponential functions. sin x - ,xi - -xi 2i exi+e-xi cos x - sinh x -~ - 2 ex-e--y 2 REFERENCES Balfour, A.
6) 2. ) ... ( a - b ) = (~,+Aa)-(x,-Ab) or (a-b)-(xa-Xb) ... A(a-b) = Aa+Ab = Aa+Ab For correlated terms, a = (x, +Aa) b = (Xb+Ab) ... (a-b) = (x,+Aa)-(~,+Ab) or (u-~)-(x,-x& = Aa-Ab A(a-b) = (Au-Ab) Rule 3 The relative error of a sum lies between the greatest and least relative errors of the terms + Au2 -I-Au3 f ... a, + a 2 + a 3 + . . xb) = (a +Aa) (b+Ab) = ( a . b)+aAb+bAa+AaAb 34 APPROXIMATE METHODS IN ENGINEERING DESIGN . . (x, . xb - a . e. A ( a . e. 6(a. b) = 6a+6b Note. For correlated variables the errors are in the same direction and for independent ones they can be in either direction; the largest error arises when they are in the same direction as in proof above.
Draw the square section to scale. 2. 9). B. Due to symmetry points in one quadrant only need to be dealt with. Case A 16 square grid, h, and since we have for point (1) and since = $a. 21) we get for point (0) 28 APPROXIMATE METHODS IN ENGINEERING DESIGN 1. 375h; GO 4% = 0 (for a 16 square matrix) (Aiv) Case B 36 square matrix h, = 4 6 . 1925 2 . . e. 7% higher. 2. Approximate computations. 3. Relationships between trigonometric and exponential functions. sin x - ,xi - -xi 2i exi+e-xi cos x - sinh x -~ - 2 ex-e--y 2 REFERENCES Balfour, A.
Approximate Engineering Methods Design by T.T. Furman (Eds.)