Introduction to Analysis of the Infinite

Book I
1988
ISBN: 978-0-387-96824-7
Verlag: Springer

Buch, Englisch, 327 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1470 g

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."

Zielgruppe

Research

Autoren/Hrsg.

Euler, Leonhard

Weitere Mitwirkende

Blanton, J.D.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis

Inhaltsverzeichnis

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.