Selected Examples in Calculus of Several Variables

This book contains many selected examples and counterexamples concerning several variables functions. Counterexamples form a fascinating part of Mathematics. The study of the Mathematics, often based on the reading of a lengthy sequence of Theorems and of their proofs, becomes more stimulating as soon as the reader tries to simplify the proofs, or conjectures that the list of the assumptions can be reduced. Counterexamples clearly show that the conjecture is false, and are a very useful tool in the understanding of Mathematics. Also, whenever the student is not able to give a rigorous proof of his conjecture, he can try to find a counterexample, and this activity is even more challenging.