Taylor's Theorem - A Selection of Classic Mathematical Articles Containing Examples and Exercises on the Subject of Algebra (Mathematics Series)

One theorem turns an awkward function into a plain sum of powers, and with it a great deal of physics and engineering becomes calculable. These classic lessons show how it is done.

Brook Taylor published the result in 1715, and it has anchored the study of series ever since. Taken from the analysis texts and teaching manuals of the years before the First World War, Taylor's Theorem gathers the chapters that set out the expansion of a function about a point, the special case at zero known as Maclaurin's series, the form of the remainder, and the conditions under which an expansion may be relied upon. Standard expansions are derived and then put to work.

Written for readers meeting the theorem for the first time, the articles go slowly and give their working in full, with problems at the close of each section. Each piece is reprinted with details of the source it came from, so the volume serves both as a way into the topic and as a record of how it was once taught.

This edition features:

• Articles on Taylor's theorem taken from analysis texts and teaching manuals of the years before 1914
• The expansion of a function about a point, with Maclaurin's series treated as the special case
• The remainder term and the conditions under which an expansion may be relied upon
• Standard expansions derived in full and then applied to worked problems
• A source note against each article, recording the volume it was taken from