A typical source of mistakes that frequently lead to a wrong or
incomplete solution for the antiderivative of a given real function
of one real variable is a misuse of the technique of change of
variable. The increasing implementation of software in apparently
mechanic tasks such as the calculation of antiderivatives has not
improved the situation, yet those software packages issue generic
warnings such as "the answer's is not guaranteed to be continuous"
or "the solution might be only valid for parts of the function".
The practical meaning of those vague machine messages is clearly
envisaged in this book, which shows how to handle the technique of
change of variable in order to provide correct solutions. This book
is monographically focused on elementary antidifferentiation and
reasonably self-contained, yet it is written in a "hand-book"
style: it has plenty of examples and graphics in an increasing
level of difficulty; the most standard changes of variable are
studied and the hardest theoretic parts are included in a final
Appendix. Each practical chapter has a list of exercises and
solutions. This book is intended for instructors and university
students of Mathematics of first and second year.
General
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