Permissions beyond the scope of this license may be available at
arnold@uark.edu
Permissions beyond the scope of this license may be available at
arnold@uark.edu
Notation used in the course (could skip)
Basic Introduction to Programming in Matlab
Pictures of a (toy) Floating point system
Comparing reals and comparing floats
Three perspectives on cancellation
Polynomials (could skip)
Rate of Convergence - the 'Big O' notation
Polynomials are Vectors (could skip)
Fundamental Theorem of Algebra (could skip)
Solving equations in one variable
Newton's method convergence analysis
Secant method convergence analysis
The Geometry of Newton & Secant
Compare Bisect, Newton & Secant
Hybrid methods for root finding
Roots of a polynomial (Mueller's method and deflation)
Conditioning and Backward stability
Evaluating the Interpolator (Barycentric weights)
Interpolation Nodes (could skip)
Lagrange interpolation example
Lagrange Chebyshev nodes example
Hermite interpolation on 2 nodes (could skip)
Kissing (osculating) polynomials
FFT Tease (could skip)
Least squares (could skip)
Numerical differentiation is easy
Numerical differentiation is hard
Optimal Quadrature (Gaussian Quad) (could skip)
Rejected (rejection sampling) (could skip)
Smart numerical integration (adaptive)
Adaptive quadrature: recursive m-file
Can we solve this IVP? (well-posed)
Linear Shooting (take-home hint?)