Introduction to Analysis of the Infinite: Book I

ISBN-13: 9781461269885 / Angielski / Miękka / 2013 / 327 str.

Leonhard Euler; J. D. Blanton

Opis

From the preface of the author: ..".I have divided this work into two books; in the first of these I have confined myself to those matters concerning pure analysis. In the second book I have explained those thing which must be known from geometry, since analysis is ordinarily developed in such a way that its application to geometry is shown. In the first book, since all of analysis is concerned with variable quantities and functions of such variables, I have given full treatment to functions. I have also treated the transformation of functions and functions as the sum of infinite series. In addition I have developed functions in infinite series..."

Spis treści

I. On Functions in General.- II. On the Transformation of Functions.- III. On the Transformation of Functions by Substitution.- IV. On the Development of Functions in Infinite Series.- V. Concerning Functions of Two or More Variables.- VI. On Exponentials and Logarithms.- VII. Exponentials and Logarithms Expressed through Series.- VIII. On Transcendental Quantities Which Arise from the Circle.- IX. On Trinomial Factors.- X. On the Use of the Discovered Factors to Sum Infinite Series.- XI. On Other Infinite Expressions for Arcs and Sines.- XII. On the Development of Real Rational Functions.- XIII. On Recurrent Series.- XIV. On the Multiplication and Division of Angles.- XV. On Series Which Arise from Products.- XVI. On the Partition of Numbers.- XVII. Using Recurrent Series to Find Roots of Equations.- XVIII. On Continued Fractions.

O autorze

Der Schweizer Mathematiker, Natur- und Technikwissenschaftler Leonhard Euler (1707-83) prägte mit seinen wegweisenden Resultaten zur Zahlentheorie, Geometrie, Reihenlehre und zur Theorie der Differentialgleichungen die Mathematik seiner Zeit. Euler gilt als bedeutender Vertreter einer mathematisch orientierten Naturwissenschaft, er lieferte u.a. fundamentale Ergebnisse zur Hydrodynamik und zur Mechanik. Zahlreiche Symbole und Bezeichnungen, die nach wie vor in verschiedenen Disziplinen Geltung haben, wurden von Euler eingeführt.