udemy-linear-algebra-and-geometry-3-2021-10-1

relations, dynamical systems, Markov matrices\ 5:07 Continuous versus discrete 17:18 Two famous examples of recurrence 29:37 Linear discrete dynamical systems 43:42 Systems of difference equations, Problem 1 1:08:21 Systems of difference equations, Problem 2 1:27:09 Systems of difference equations, Problem 3 1:36:19 Higher order difference equations, Problem 4 1:53:56 Higher order difference equations, Problem 5 2:09:07 Higher order difference equations, Problem 6 2:27:29 Markov matrices 2:38:47 Each Markov matrix has eigenvalue 1 2:43:34 Steady-state vector (equilibrium vector), Problem 7 3:17:58 Markov matrices, Problem 8, Restaurant 3:42:22 Markov matrices, Problem 9, Migration 3:56:43 Markov matrices, Problem 10, Election 4:15:23 Dynamical systems, Problem 11 4:27:59 Where to read more on this topic systems of linear ODE, and solving higher order ODE\ 4:30:43 What is an ODE and what kinds of ODE we are going to deal with 4:46:12 Solutions to first order linear ODE with constant coefficients 4:54:22 Systems of first order linear ODE with constant coefficients 5:16:10 A very simple example 5:25:11 The method 5:59:13 System of ODE, Problem 1 6:10:37 System of ODE, Problem 2 6:19:22 System of ODE, Problem 3 6:34:16 How to deal with higher order linear ODE 6:53:06 Another way of looking at the same problem product as a generalization of dot product\ 7:20:24 Between concrete and abstract 7:24:02 Dot product in Part 1 7:33:16 Dot product and orthogonality in Part 2 7:38:13 From R^2 to inner product spaces 7:44:26 Inner product spaces 8:07:34 Euclidean n-space 8:15:56 A very important remark about notation 8:19:53 Inner and outer products 8:24:15 Weighted Euclidean inner product, Problem 1 8:41:11 Remember transposed matrices 8:45:48 Positive definite matrices 8:59:27 Quadratic forms and how to read them 9:18:16 Matrix inner products on R^n, Problem 2 9:40:19 Gram matrix, Problem 3 10:15:16 Gram matrix, Problem 4 10:24:12 Inner product in the space of continuous functions 10:34:57 Gram matrix for an inner product in the space Pn of polynomials 11:06:29 Two inner products on the space of polynomials Pn 11:19:35 The evaluation inner products on P2, Problem 5 11:33:01 Inner product in the space of m × n matrices 11:39:36 Inner product in the space of square matrices 11:51:46 Inner product in the space of matrices, Problem 6