The equations of the unsteady, incompressible laminar boundary layer are considered in the case of two-dimensional flow and in the presence of a pressure gradient. The fundamental equations are cast into a more manageable form through the expansion of the unknown velocity by Taylor’s formula, in terms of a suitable variable. Consideration is also given to the truncation error. Several examples were carried out to show that even the first term in Taylor’s formula provides good accuracy in many circumstances.

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