CFE

Calculus for Engineering

Objectives

• Apply continuity and differentiability results to study properties and sketch graphs of real functions.
• Calculate primitives of functions applying the techniques studied.
• Apply the concept of integral to calculate areas and lengths of curves.
• Calculate improper integrals.
• Apply convergence criteria to numerical series.
• Analyze the convergence of power series.

Program

Real functions of one real variable Basic concepts of function. Relative and absolute extrema. Limits and continuity. Composition and inversion of functions. Derivative of a function; geometric interpretation. Taylor polynomial. L’Hôpital rule. Primitives, definition and properties. Indefinite integrals. Immediate integrals. Integration by parts and by change of variables. Integration of rational functions. Riemann integral, definition and properties. Fundamental theorems of calculus. Computation of areas and length of curves. Improper integrals. Numerical series, definition and properties. Convergence of series. Convergence criteria. Power series, definition and properties. Radius and interval of convergence. Taylor series.

Bibliography

Apostol, T. (1991), Cálculo Vol. I, Reverté. Campos Ferreira, J. (2011), Introdução à Análise Matemática, Fundação Gulbenkian. Marsden, J., Weinstein, A. (1985). Calculus I and Calculus II (2nd ed.), New York: Springer-Verlag. Stewart, J. (2006), Cálculo (5th ed.), S. Paulo: Thompson.