Many situations of interest to researchers require solutions to equations that cannot be solved exactly or are too complicated to be modeled quickly and easily. An example of the latter is the three-dimensional simulation of particle motion in flowing liquids. In situations like this, computational methods are used to produce theoretical models that provide behavioral insight and predictive power under new conditions.

It's not unusual for introductory courses in computational methods to be tied in with a numerical computing platform like MATLAB, covering the following topics:

  • Solutions of nonlinear equations
  • Solutions of linear systems
  • Interpolation and polynomial approximation
  • Curve fitting
  • Numerical differentiation
  • Numerical integration
  • Numerical optimization
  • Solution of differential equations
  • Solution of partial differential equations
  • Eigenvalues and Eigenvectors

An excellent journal for computational methods is the Journal of Computational and Applied Mathematics. There are many good books on the topic of computational methods, and some useful online tutorials.

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