Calculus in one real variable

Basic information


90 hours


Does not exist


Functions: exponential, logarithmic, polynomial, trigonometric, linear. Domain, image, crescente and decrescent, even, odd, inverse function. Rate of change; Limits; precise definition of limit; continuity. Derivatives; differentiation rules; chain rule; implicit derivation; L’Hôpital rule; superior derivatives; related fees; linear approximations; differentials; Taylor polynomial; Average Value Theorem; Maximum and minimum; convex and concave functions; graphics; optimization problems. Anti-derivatives; areas and distances. Riemann sums. Defined integral. Fundamental Theorem of Calculus. Undefined integrals. Integration by substitution and by parts. Integrals of rational functions by partial fractions. Improper integrals.


Teaching Plan



•    Stewart, James. Calculus. Volume 1. Cengage Learning;
•    Ávila, Geraldo. Calculus 1: one variable functions. Technical and Scientific Books, 1994;
•    Morettin, P.A .; Hazzan, S.; Bussab, W .. Calculus: one and multiple variables functions. Saraiva, 2003.


•    Leithold, Louis, Calculus with Analytical Geometry. Harbra;
•    Apostol, Tom M .. Calculus, Blaisdell;
•    Thomas, George B. Calculus. Pearson;
•    Pereira, Iaci Malta. Calculus in One Real Variable, volume 1: an introduction to Calculus. Matmedia;
•    Pereira, Iaci Malta. Calculus in One Real Variable, volume 2: derivative and integral. Matmedia