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 . 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...

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 . 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...