Author | Euler. author |
---|---|

Title | Introduction to Analysis of the Infinite [electronic resource] : Book I / by Euler |

Imprint | New York, NY : Springer New York : Imprint: Springer, 1988 |

Connect to | http://dx.doi.org/10.1007/978-1-4612-1021-4 |

Descript | XV, 327 p. online resource |

SUMMARY

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..."

CONTENT

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

Mathematics
Functions of real variables
Mathematics
Real Functions