Introduction to Analysis of the Infinite: Book I

Euler, Leonhard

ISBN 10: 1461269881 / ISBN 13: 9781461269885

Editore: Springer, 2013

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Dati bibliografici

• Titolo: Introduction to Analysis of the Infinite: Book I
• Editore: Springer
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 1461269881
• ISBN 13: 9781461269885
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

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..."

Contenuti

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.