University of Michigan - Shanghai Jiao Tong University Joint Institute

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Vv471: Introduction to Numerical Methods


Prerequisites: Vg101; and Vv256 or Vv286
Background and Goals: This is a survey of the basic numerical methods which are used to solve scientific problems.
The emphasis is evenly divided between the analysis of the methods and their practical applications. Some
convergence theorems and error bounds are proved. The course also provides an introduction to MATLAB, an
interactive program for numerical linear algebra, as well as practice in computer programming. One goal of the
course is to show how calculus and linear algebra are used in numerical analysis.
Content: Topics may include computer arithmetic, Newton’s method for non-linear equations, polynomial
interpolation, numerical integration, systems of linear equations, initial value problems for ordinary differential
equations, quadrature, partial pivoting, spline approximations, partial differential equations, Monte Carlo methods,
2-point boundary value problems, Dirichlet problem for the Laplace equation.
Alternatives: Vv371 (Numerical Methods) is a less sophisticated version. Only one class (Vv371 or Vv471) can
be taken for credit.