Numerical Methods and Nonlinear Optimization.

Objectives

  • Analyze engineering problems;
  • Use numerical techniques for modeling physical problems;
  • Solve engineering problems using numerical methods;
  • Implement numerical algorithms;
  • Compare different methods and optimization algorithms in solving numerical problems;
  • Assess numerical results;
  • Use of numerical software.

Program

  • Errors and stability.
  • Numerical solving of nonlinear equations.
  • Direct methods for solving linear systems.
  • Numerical solving of nonlinear equation systems (Newton’s method).
  • Least squares approximation (linear model): polynomial and non-polynomial model.
  • Polynomial interpolation: Newton’s polynomial and splines.
  • Numerical integration.
  • Nonlinear optimization problem. Optimality conditions.
  • Optimization algorithms with and without derivatives
  • Use of numerical computing software.

Bibliography

S.C. Chapra e R.P. Canale, Numerical Methods for Engineers (8th edition), McGraw-Hill, 2020. S.C. Chapra, Applied Numerical Methods W/MATLAB: for Engineers & Scientists (3rd Edition), McGraw-Hill, 2012. Chapra, S., Applied Numerical Methods with Python for engineers and scientists. McGraw-Hill, 2021. J. Nocedal, S.J. Wright, Numerical Optimization, Springer Series in Operations Research, Springer, New York, NY, 2006. D. Bertsekas, Nonlinear Programming, Athena Scientific, 2016.

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