EAN: 9781493946815

UNDERGRADUATE TEXTS IN MATHEMATICS MORE CALCU...

This book goes beyond the basics of a first course in calculus to reveal the power and richness
of the subject. Standard topics from calculus - such as the real numbers  differentiation and
integration  mean value theorems  the exponential function - are reviewed and elucidated before
digging into a deeper exploration of theory and applications  such as the AGM inequality 
convexity  the art of integration  and explicit formulas for pi. Further topics and examples
are introduced through a plethora of exercises that both challenge and delight the reader.
While the reader is thereby exposed to the many threads of calculus  the coherence of the
subject is preserved throughout by an emphasis on patterns of development  of proof and
argumentation  and of generalization. More Calculus of a Single Variable is suitable as a text
for a course in advanced calculus  as a supplementary text for courses in analysis  and for
self-study by students  instructors  and  indeed  all connoisseurs of ingenious calculations.

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