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Essential Mathematical Methods for the Physical Sciences by K. F. Riley, M. P. Hobson

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A

Review of background topics

A.1  Arithmetic and geometry

  1. Logarithms and the exponential function

    For a logarithm to any base a (> 0), x = aloga x and

    •  For x > 0, its natural logarithm, loge x ≡ ln x is defined by x = eln x, where e = exp(1) and

    •  The exponential function and natural logarithm have the properties

  2. Rational and irrational numbers

    •  If is irrational, implies that a = c and b = d.

    •  To rationalize , write it as

  3. Physical dimensions ...

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