Advanced Topics in Mathematical Modeling

Mathematical analysis applied to systems modeling: Theory, methods and applications.

Mathematical foundations of probability theory. Convergence of probability measures and limit theorems. Probabilistic models. Applications in the modeling of random systems. Finite-dimensional vector spaces. Transformations. Space with inner product. Spectral Theorem. Applications.

Additional topics depending on the specific course offering.

Basic Information

Workload
45

Bibliografia Obrigatória:

  • Frank R. Giordano, Maurice D. Weir. A First Course in Mathematical Modeling.. Brooks/Cole Pub. Co., 1985
  • Rudin, Walter. Principles of mathematical analysis. Vol. 3. New York: McGraw-hill, 1964.
  • Grimmett, Geoffrey, and David Stirzaker. Probability and Random Processes. 3rd ed. Oxford University Press, 2001
  • Paul R. Halmos . Finite-Dimensional Vector Spaces: Second Edition. 1993 7.

Bibliografia Complementar:

  • John Haig. Probability Models. Springer Undergraduate Mathematics Series. 2nd ed. 2013
  • Trefethen, L. N., & Bau, D. Numerical Linear Algebra. SIAM. 1997
  • Rudin, W., Real and Complex Analysis, McGraw-Hill Book Company Inc., New York-Toronto-London, 1974.
  • Nicholas J. Higham, Mark R. Dennis, Paul Glendinning, Paul A. Martin, Fadil Santosa, Jared Tanner. The Princeton Companion to Applied Mathematics. 2016