🇵🇹 PT

Objectives

  • Interpret the concepts of continuity and differentiability of functions of multiple variables;
  • Classify constrained and unconstrained extreme of functions of multiple variables;
  • Calculate multiple integrals;
  • Interpret the notions of double and triple integrals in the calculation of areas and volumes;
  • Calculate line and surface integrals.

Program

  • Functions of multiple real variables. Domains, graphics and level sets. Limits and continuity. Partial and directional derivatives. Gradient and derivative. Derivative of the composition of functions.
  • Taylor’s polynomial. Local and conditional maxima and mínima of real functions.
  • Multiple integrals: areas, volumes and change of coordinates. Parametrisation of curves. Line and surface integrals. Green, Stokes and Gauss Theorems

Bibliography

  • Marsden, J.E. & Tromba, A. (2003). Vector Calculus (5th ed.). New York: W.H. Freeman.
  • Stewart, J. (2006) Cálculo (5a ed.). São Paulo: Thomson.
  • Apostol, T. (1991), Cálculo Vol. I, II, Reverté.

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