Introduction to the Theory of Programming Languages by Bertrand Meyer

By Bertrand Meyer

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By adding all the small regular shapes together to make the larger shape, the large shape suddenly becomes manageable. 16 shows the idea. These infinitesimal rectangles effectively simulate the shape of the curved path There are only 40 rectangles under this curve and the error is very small. 16 A curve described by multiple rectangles If you think of the large irregular shape as being caused by something in the real world that continually changes direction with time, such as the path of a cannonball fired off a cliff at a passing ship, then you can see the advantages.

2 Type 2: Linear procedural problems Their main feature is the existence of procedural constraints controlling what can be done to further define the problem and then solve it. Don’t confuse these with administrative constraints; they are established procedural constraints of the technical world (Fig. 2). The methodology is to use procedural techniques to solve the problem rather than approaching it in an overly technical way. The problem is still in linear form, so you have to work through the steps one-by-one, without being retrospective (or you will lose confidence).

E. n ¼ m/r The SI unit is m2/s. Other imperial and CGS units are also used. 4 Consistency of units Within any system of units, the consistency of units forms a ‘quick check’ of the validity of equations. The units must match on both sides. Example: To check kinematic viscosity (n)¼ dynamic viscosityðmÞ density ðrÞ m2 Ns m3 ¼ 2Â s kg m Replacing N with kgm/s2 m2 kgm s m3 ¼ 2 2 Â s m s kg Units 33 Cancelling gives m2 m4 s m2 ¼ 2 2¼ s s s m OK, units match. 1 Foolproof conversions: using unity brackets When converting between units it is easy to make mistakes by dividing by a conversion factor instead of multiplying, or vice versa.

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