P. Habala, DEN-01f: Numerical analysis – Numerical integration (quadrature) скачать в хорошем качестве

P. Habala, DEN-01f: Numerical analysis – Numerical integration (quadrature)

“Differential equations and numerical analysis” is a course offering a basic overview of these two fields. The original lectures were partially reshot and augmented to offer more for those who need to/like to explore the topics further. [0:00:00] Numerical integration: basic setup, rectangle methods [0:15:54] Local and global error, derivation via Taylor expansion [0:35:16] Musings on errors, order of method, order of relative error [0:45:51] Numerical stability, summary of numerical integration concepts [0:48:39] The trapezoid method [1:00:25] Derivation of method via Taylor expansion and error optimization [1:12:10] Interpretation of error, prediction, experiments [1:17:54] The Simpson method, derivation using error optimization [1:43:31] Error of method, experiments [1:49:06] Bonus: Richardson extrapolation for integrals, Romberg integration [1:54:14] Predicting error based on Richardson extrapolation and knowledge of order [2:02:22] Bonus: some other integration ideas (midpoint, Gauss, Monte Carlo) Complete playlist:    • doc. P. Habala: Differential equations & n...