Functions and Infinite Series

he expression cos(pi/9) is a symbol. It describes the ratio of two straight segments, but not the value of this ratio. This value is the limit of the series 1-(pi/9)^2/2! + (pi/9)^4/4! - (pi/9)^6/6! + ...... The twin, function-series, became the most famous pair of Analysis, though still the foundations of the calculus remained unclear. In this book, the author attempted to expound the most useful facts about Taylor series of real and complex variables, as well as about Fourier transforms and Fourier series, as a mathematical narrative, in a semi-popular design. This book is not intended for specialists in mathematics and rather for those whose mathematical background is no further than the traditional second year University course in mathematics.

Autorentext

George Mpantes is a high school mathematics teacher. He writes articles in academia.edu, and has published four books in Greek and English. In his works G. Mpantes acquaints the layman with the historical development and basic meaning of the momentous theories and discoveries in mathematics and physics.

Klappentext

he expression cos( /9) is a symbol. It describes the ratio of two straight segments, but not the value of this ratio. This value is the limit of the series 1-( /9)^2/2! + ( /9)^4/4! - ( /9)^6/6! + ...... The twin, function-series, became the most famous pair of Analysis, though still the foundations of the calculus remained unclear. In this book, the author attempted to expound the most useful facts about Taylor series of real and complex variables, as well as about Fourier transforms and Fourier series, as a mathematical narrative, in a semi-popular design. This book is not intended for specialists in mathematics and rather for those whose mathematical background is no further than the traditional second year University course in mathematics.