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Scientific Computing Pages (one page at a time)
Programming
Basic computer programming constructs
Properties of good code
Basic Introduction to Matlab
Matlab function m-file
A Matlab machine precision m-file
Finite Precision Floating Point Arithmetic
Floating point representation
A Toy Floating Point System
Reals and Floats
Comparing Numbers
Floating point arithmetic
Swamping and Cancellation
Floating point linear algebra
On evaluating a function
Curve Fitting and Approximation
Taylor Polynomial
Taylor Polynomial Picture
Polynomial Interpolation
An example of Lagrange interpolation
More Polynomial Interpolation
Kissing Polynomials
FFT Tease
Piecewise Polynomial Interpolation
Least Squares Polynomials
Examples of Least Squares Polynomials
Equations in One Variable
Implementing the quadratic formula?
Finding Roots
Rate of Convergence
Order of Convergence
Method of Bisection
Newton's Method
Secant Method
Convergence of the Secant Method
Newton and Secant example
Compare Bisect, Newton & Secant
Hybrid Methods
Roots of Polynomials
Example of Polynomial Roots in FP
Evaluating Polynomials
Gaussian Elimination Ax = b
An outline of your first linear algebra course
Matrix Multiplication
Coordinates
A 2x2 example
Triangular Systems
Gaussian Elimination as a Matrix Factorization
Gaussian Elimination Process
Gaussian Elimination with Partial Pivoting
Errors in Gaussian Elimination
The Ax=b residual vector
An Alternative Triangular Factorization
Definition of FLOP
Vector Norms
Matrix Norms
Condition analysis
Conditioning of Addition
Conditioning and Stability
Conditioning and Stability again
Linear Least Squares
Inner Products
Orthogonal Projections
Singular Value Decomposition
Least Squares Approximation
Normal Equations
Cholesky Factorization
Least Squares Computations
Sensitivity of LS
Sensitivity of LS details
Gram Schmidt QR
Gram Schmidt with Rounding Errors
Gram Schmidt and Least Squares
Householder Reflectors
Householder QR Impementation
Householder Factored-Q Matrix
QR Factorizations
Differentiation and Integration
Numerical Differentiation
Numerical Differentiation in FP
Numerical Integration
Composite Newton-Cotes
Optimal Quadrature
Adaptive Quadrature
Recursive m-file for Adaptive Quadrature
Monte-Carlo integration
Monte-Carlo Rejection
ODE's
Well-posed Initial Value Problems
The Initial Value Problem and Euler's method
Euler's method graphically
Local Truncation Error
Runge-Kutta Methods
Runge-Kutta Methods order 2
Adaptive Runge-Kutta Methods
Multistep Methods
Adaptive Multistep Methods
Stiff Differential Equations
Systems of Differential Equations
Example System
The shooting method for boundary value problems
Eigenvalues
The Power Method
The Inverse Power Method
Convergence of Power Iterations
The Hessenberg Matrix
QR Iterations
The Francis QR Step
The Sensitivity of Eigenvalues
Arnoldi: some theory
f(A) for diagonalizable A
f(Jordan block)
PDE's
Finite Difference: Parabolic