This book provides a one-semester undergraduate introduction to counterexamples in calculus and analysis. It helps engineering, natural sciences, and mathematics students tackle commonly made erroneous conjectures. The book encourages students to think critically and analytically, and helps to reveal common errors in many examples. It is intended for students who are interested in developing a deeper understanding of the topics of calculus. The gathered counterexamples may also be used by calculus instructors in their classes.

Andrei Bourchtein, Ludmila Bourchtein

FUNCTIONS OF ONE REAL VARIABLE. Elementary properties of functions. Limits. Continuity. Differentiation. Integrals. Sequences and series. FUNCTIONS OF TWO REAL VARIABLES. Limits and continuity. Differentiability. Integrability.