Calculus in one real variable

Basic information

Workload: 

90 hours

Prerequisite: 

Does not exist

Syllabus: 

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

Bibliography

Mandatory: 

•    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.

Complementary: 

•    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