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L {e a t sin(bt)} = L {e a t cos(bt)} =

Maurice Halstead was one of the rst researchers in software metrics. He did his work in the late 1960s and 1970s. His goal was to identify what contributed to the complexity in software. He empirically looked for measures of intrinsic size. After nding what he felt were good measures and prediction formulas, he tried to develop a coherent theory. His simple metrics are still considered valid, while his more complex metrics and prediction formulas have been found to be suspect.

{ f (t )} + b L {g(t )}

Currently, the only setting that affects your Maps app is Location Services, which is critical for determining your current location. 1. 2. Touch the Settings icon. Tap the General tab in the left column. Now find the Location Services switch about halfway down. Move this switch to the ON position so that Maps can approximate your location.

{ f (t )} , then L {ea t f (t )} = F (s a)

Mathematica computes the Laplace transform of a function, f, by the invocation of the command LaplaceTransform.

NOTE: Keeping the Location Services switch ON will reduce battery life by a small amount. If you never use Maps or care about your location, set it to OFF to save your battery life.

LaplaceTransform[f[var1], var1, var2] computes the Laplace transform of the function f, with independent variable var1, and expresses it as a function of var2.

The basic approach that gave Halstead good results was to consider any program to be a collection of tokens, which he classi ed as either operators or operands. Operands were tokens that had a value. Typically, variables and constants were operands. Everything else was considered an operator. Thus, commas, parentheses, arithmetic operators, brackets, and so forth were all considered operators. All tokens that always appear as a pair, triple, and so on will be counted together as one token. For example, a left parenthesis and a right parenthesis will be considered as one occurrence of the token parenthesis. A language that has an if-then construction will be considered to have an if-then token. Halstead also was concerned about algorithms and not about declarations, i/o statements, and so on. Thus, he did not count declarations, input or output

LaplaceTransform[Exp[2t] Sin[3t], t, s] //ExpandDenominator 3 13 4 s + s2 LaplaceTransform[Exp[2t]Cos[3t], t, s] //ExpandDenominator 2 + s 13 4 s + s2 LaplaceTransform[a f[t] + b g[t], t, s] a LaplaceTransform[f[t], t, s] + b LaplaceTransform[g[t], t, s] LaplaceTransform[f'[t], t, s] f[0] + s LaplaceTransform[f[t], t, s] LaplaceTransform[f''[t], t, s] s f[0] + s2 LaplaceTransform[f[t], t, s] f'[0]

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The power of the Laplace transform is derived from the fact that there is a one-to-one correspondence between f (t) and L { f (t )}. This means that if L { f (t )} is known, then f (t) is uniquely determined. If F (s) = L { f (t )}, then f (t ) = L 1 { F (s)}. L 1 is called the inverse Laplace transform.

InverseLaplaceTransform[F[var1], var1, var2] computes the inverse Laplace transform of the function F, with independent variable var1, and expresses it as a function of var2.

statements, or comments. However, currently most organizations would count all parts of a program. Halstead s de nitions of operator and operand are open to many interpretations. No standard has been accepted for deciding ambiguous situations. The good news is that as long as an organization is consistent, it doesn t matter. The bad news is that people in one organization cannot compare their results with the results from other organizations. The author recommends a syntax-based approach where all operands are userde ned tokens and all operators are the tokens de ned by the syntax of the language.