Mathematical Analysis for Engineering

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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