Trapezoidal rule that Monte-Carlo integration is most likely a better choice, but for 2 and 3 dimensions, equispaced sampling is efficient. This is exploited in computational solid state physics where equispaced sampling over primitive cells in the reciprocal lattice is known as "Monkhorst-Pack integration". For various classes of functions that are not twice-differentiable, the trapezoidal rule has sharper bounds than Simpson's rule. The trapezoidal rule is one of a family of formulas for numerical integration called Newton–Cotes formulas, of which the midpoint rule is similar to the trapezoid rule. Simpson's rule is another member of the same family, and in general has
Punctuation two styles differ mainly in the way in which they handle quotation marks, particularly in conjunction with other punctuation marks. In British English, punctuation such as periods and commas are placed outside the closing quotation mark; in American English, however, punctuation is placed inside the closing quotation mark. This rule varies for other punctuation marks; for example, American English follows the British English rule when it comes to semicolons, colons, question marks, and exclamation points. Other languages of Europe use much the same punctuation as English. The similarity is so strong that the few variations may confuse a native English