Taylor Series and Coordinate Systems | Fields and Waves Ep 3

Taylor series and convergence, then Cartesian, cylindrical and spherical coordinates. It derives the gradient, divergence, curl and Laplacian in curvilinear coordinates. Chapters: 0:00 Intro 0:28 Motion and small changes 1:40 Taylor series 2:50 Convergence 3:57 Example: a bouncing approximation 4:58 Cartesian coordinates 6:25 Cylindrical coordinates 7:33 Spherical coordinates 8:38 Unit vectors 9:54 Line, area and volume elements 10:33 Gradient in curvilinear coordinates 12:16 Gradient in spherical coordinates 13:29 Divergence from shells 15:21 Divergence in spherical coordinates 16:33 Divergence in cylindrical coordinates 17:46 Curl 19:15 The Laplacian 20:16 Recap Made for TU Delft Fields and Waves revision. Course material: https://bscect.github.io/FieldWaves/main/i... Self-test answers are not included in this description.