Numerical Methods

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Most equations in science and engineering defy analytical solution. But they can be evaluated numerically, resulting in approximate values for the unknown variable. The underlying computational approach is not unique. There are many ways to discretize operators and design recurrence formulas. Our course covers basic numerical methods for root finding, discretization of integrals, and discretization of derivatives. In particular, we focus on finite-difference schemes for ordinary and partial differential equations. This is done in the context of engineering physics, with proper balance between programming practice and analysis of stability, consistency, and convergence of the methods.