Infinite series | Math History | NJ Wildberger

Video Description

We discuss various uses of infinite series in the 17th and 18th centuries. In particular we look at the geometric series, power series of log, the Gregory-Newton interpolation formula, Taylor's formula, the Bernoulli's, Eulers summation of the reciprocals of the squares as pi squared over 6, the harmonic series, product expansion of sinx, the zeta function and Euler's product expansion for it, the exponential function, complex values and finally the circular functions too! Video Contents: 00:00 Infinte series 00:46 18th century mathematicians 02:40 Geometric series 03:40 Infinite polynomials 09:49 Gregory Newton Interpolation Formula 18:02 Taylor's Theorem 22:50 Leonard Euler Basel - Berlin -St Petersburg 25:11 Introduction to Analysis Infinitorum 1748 29:48 Descartes' Factor theorem 42:58 Bernoulli numbers ( James Bernoulli -Probability) 46:58 The zeta function 53:29 The Riemann Hypothesis 1:03:00 Euler's formula for complex exponential ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated.