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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
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
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
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
Über den Autor
JOSEPH ADDISON How shall I bring to your mind the time and distance that separate us from the Age of Fable? Think of what seemed to you the longest week of your life. Think of fifty-two of these in a year; then think of two thousand five hundred years and try to realize that Aesop-sometimes called the Eighth Wise Man-lived twenty-five centuries ago and made these wonderful tales that delight us to-day. Shakespeare is even yet something of a mystery, although he was born in our own era, less than five hundred years ago; but men are still trying to discover any new facts of his life that might better explain his genius. A greater mystery is grand old Homer, who has puzzled the world for centuries. Scholars are not certain whether the "Iliad" or "Odyssey" are the work of one or more than one mind. Who can say? for the thrilling tales were told-probably after the fashion of all the minstrels of his day-more than eight hundred years before Christ. On the background of that dim distant long ago, perhaps two hundred years later than Homer, looms the magnificent figure of another mysterious being-Aesop the Greek slave. Wherever and whenever he lived, and whether, in fact, he ever lived at all, he seems very real to us, even though more than two thousand years have passed. Among all the stories that scholars and historians have told of him-sifting through the centuries the true from the false-we get a vivid picture of the man. He was born in Greece, probably in Phrygia, about 620 years before Christ. He had more than one master and it was the last, Iadmon, who gave him his liberty because of his talents and his wisdom. The historian Plutarch recounts his presence at the court of Croesus, King of Lydia, and his meeting Thales and Solon there, telling us also that he reproved the wise Solon for discourtesy toward the king. Aesop visited Athens and composed the famous fable of Jupiter and the Frogs for the instruction of the citizens. Whether he left any written fables is very uncertain, but those known by his name were popular in Athens when that city was celebrated throughout the world for its wit and its learning. Both Socrates and Plato delighted in them; Socrates, we read, having amused himself during the last days of his life with turning into verse some of Aesop's "myths" as he called them.
Details
| Erscheinungsjahr: | 2012 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Importe, Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Titel: | Taylor's Theorem - A Selection of Classic Mathematical Articles Containing Examples and Exercises on the Subject of Algebra (Mathematics Series) |
| Inhalt: | Kartoniert / Broschiert |
| ISBN-13: | 9781447456971 |
| ISBN-10: | 1447456971 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Various |
| Hersteller: | Browne Press |
| Verantwortliche Person für die EU: | Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de |
| Maße: | 216 x 140 x 5 mm |
| Von/Mit: | Various |
| Erscheinungsdatum: | 25.06.2012 |
| Gewicht: | 0,119 kg |
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