Calculus in Several Variables

Functions of several variables: partial and directional derivatives, chain rule, gradient and level set, critical points, convex and concave functions, Lagrange multipliers. Curves defined by parametric equations, tangent, arc length, areas. Multiple integrals, variables change. Line integrals. Parameterization of Surfaces. Surface integrals. Green's theorem. Stokes' theorem. Divergent’s Theorem.

Basic Information

90 hours
Calculus in one real variable


  • James Stewart. Calculus. Vol. 2. Cengage Learning, 7th edition 2013;
  • Geraldo Ávila. Calculus 3: of multiple variable functions. Technical and Scientific Books, 2006;
  • Morettin, P.A .; Hazzan, S.; Bussab, W .. Calculus: functions of one and several variables. Saraiva, 2003.


  • Carl Simon and Lawrence Blume, Mathematics for Economists, 2004;
  • Louis Leithold, Calculus with Analytical Geometry. Vol 2, Harper & Row do Brasil, 1992;
  • George B. Thomas, Calculus. Vol 2, Pearson, 2009;
  • Humberto Bertolossi, Differentiable Calculus for several variables. An Introduction to Optimization Theory, Loyola 2003;
  • Tom M. Apostol. Calculus, Blaisdell, 1969.
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