Preface Preface
The topics covered in this course can be divided into 5 units.
Matlab: Matrix/vector manipulation, matrix/vector creation, elementwise operations, built-in functions, input/output, 2d graphics, scripting, functions.
Solving equations: linear systems, bisection method, fixed point method, Newton and secant methods, multivariable Newton's method, Broyden's method.
Numerical calculus: numerical differentiation, numerical integration: trapezoidal rule, Simpson's rule, orthogonal polynomials (Legendre, Laguerre), Gaussian integration, Gauss-Laguerre integration, adaptive integration, solving ODE with Euler's method and trapezoidal method, ODE systems.
Data fitting: polynomial interpolation, spline interpolation, discrete Fourier transform, linear least squares, model comparison, nonlinear least squares, transforming data.
Optimization: linear programming, single-variable minimization, steepest descent, conjugate gradient method, Nelder-Mead method, constrained optimization, applications.
Numerical linear algebra is not included above because it is the subject of a separate course (MAT 532).
Although the course is built around Matlab software, one can use Octave to run examples and do homework just as well.
If you are new to Matlab, begin with the free online minicourse MATLAB Onramp. The first part of the course, up to and including “Plotting Data”, is the most important one. It will be referenced in each of the first four chapters/classes.