Description
Book SynopsisA 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.
Table of ContentsTheoretical Chapters: Background (Sequences of Real Numbers and Compactness); Real-Valued Functions of a Real Variable (Continuity, Differentiability and Integrability in the Sense of Riemann); Elementary Real-Valued Functions (Power Functions, Root Functions, Polynomials, Exponential, Logarithm, Circular Functions and Hyperbolic Functions); Antidifferentiation (Fundamental Results; The Technique of Change of Variable and Their Tricks); Practical Chapters: Antidifferentiation by Parts; Rational Functions; Binomial Differentials; Rational Functions of Trigonometric Arguments; Tables; and other papers; Appendix;
