Sequences of real numbers and their limits. Concept of function limit and its basic properties, fundamental limits. Continuity, properties of continuous functions. Concept of derivative and its basic properties; calculating the derivatives of elementary functions; chain rule and applications; Mean Value Theorem; Taylor polynomial; using the derivative to obtain the graph of a function. Maximum and minimum problems. Concept of integral and its basic properties; Fundamental Theorem of Calculus; integration by substitution and by parts. Areas and volumes obtained through integrals.

References:

  • Fundamentals of Calculus, PROFMAT Collection, SBM, in preparation.
  • Calculus of functions of one variable, G. Ávila, vol. 1. LTC.