Explore the fascinating world of Gaussian integrals through a comprehensive 3.5-hour tutorial covering twelve different methods of solving this fundamental mathematical concept. Delve into various approaches including polar coordinates, u-substitution, differentiation, Feynman's technique, volume calculations, and the Gamma function. Discover unique perspectives such as the Wallis, Stirling, and Ramanujan methods, as well as applications in complex analysis and Fourier transformations. Investigate challenging variations like the "impossible integral" and "Gauss cubed," and learn to identify common mistakes in Gaussian integral calculations. Master this essential mathematical tool through diverse problem-solving techniques and gain a deeper understanding of its wide-ranging applications in mathematics and physics.
Overview
Syllabus
Gaussian Integral 1 Polar Coordinates.
Gaussian Integral 2 u substitution.
Gaussian Integral 3 Differentiation.
Gaussian Integral 4 Feynman way.
Gaussian Integral 5 Volumes.
Gaussian Integral 6 Gamma Function.
Gaussian Integral 7 Wallis Way.
Gaussian Integral 8 Original Way.
Gaussian Integral 9 Stirling Way.
Gaussian Integral 10 Fourier Way.
Gaussian Integral 11 Complex Analysis.
Gaussian Integral 12 Ramanujan Way.
Impossible integral?.
Gaussian Integral.
Gauss cubed.
Gaussian #shorts.
a Gaussian mistake?.
Taught by
Dr Peyam
