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Melvin Leok @UC3x0QbvHPMEf_O0Usp4eoCQ@youtube.com

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Melvin Leok is a professor of mathematics at the University


13:20
Introduction to splines
08:45
Properties of divided differences
11:17
Newton interpolating polynomial from divided difference table
06:42
Algorithm: Divided differences
11:25
Divided differences
09:27
Newton form of interpolating polynomial
12:49
Properties of polynomial interpolation
17:07
Lagrange polynomial interpolation
18:06
Types of interpolation
08:32
Approximation vs. interpolation
10:56
Application: Roots of a complex function
08:23
Summary of numerical methods for algebraic equations
07:23
Application: Unconstrained minimization of a scalar function of several variables
05:11
Algorithm: Newton's method for systems
19:06
Nonlinear systems of equations - Newton's method
23:13
Convergence of iterative methods for systems of linear equations
09:08
Algorithm for Jacobi and Gauss-Seidel iterations
09:59
Iterative methods for systems of linear equations - Gauss-Seidel iteration
18:51
Iterative methods for systems of linear equations - Jacobi iteration
09:45
Regression with other functional forms
12:09
Normal equations for least squares regression
27:50
Least squares for regression
09:26
Algorithm for LU with partial pivoting
08:14
LU with partial pivoting in general
11:48
Pivoting and permutation matrices
21:39
Partial pivoting by example
09:39
The problem with small pivots
07:07
Summary of LU decomposition
10:21
Solving linear systems using LU decomposition
00:36
Lie group collision variational integrator - union of spheres - Example 2
05:13
LU in general
24:48
LU decomposition
21:01
Gaussian elimination
16:05
Forward and backward substitution for lower and upper triangular matrices
25:14
Review of linear algebra and systems of linear equations
11:51
Newton's method as a fixed point iteration
14:13
Fixed point theorem
11:43
Fixed points and fixed point iterations
10:36
Order of convergence for the bisection and Newton methods
09:35
Secant method for rootfinding
20:48
Newton's method for rootfinding
05:41
Motivation for the Newton method for rootfinding
08:14
Method of False Position
04:58
Algorithm: Bisection Method
10:33
Convergence rate of bisection method and stopping criteria
15:06
Bisection method for scalar, nonlinear rootfinding
12:03
Stability and Big-O notation
16:01
Floating point arithmetic
19:26
Floating point numbers
17:23
Binary numbers and errors
11:55
Truncation error for Taylor series
10:53
Proof of Taylor's theorem with integral remainder
18:24
Taylor polynomials and remainder theorem
13:59
Some important theorems from calculus: mean value theorem, intermediate value theorem
10:32
Introductory lecture: Numerical methods for physical modeling
01:23
Rolling Dice Simulation - Lie group collision variational integrator
01:42
Lie group collision variational integrator - bouncing cube/dice simulation - Example 4
01:42
Lie group collision variational integrator - bouncing cube/dice simulation - Example 3
01:42
Lie group collision variational integrator - bouncing cube/dice simulation - Example 2
01:42
Lie group collision variational integrator - bouncing cube/dice simulation - Example 1