More Calculus of a Single Variable

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 π.

Carefully dissects key concepts such as limits of sequence, convergence & divergence of monotone sequences, infinite limits, derivatives, integrals, and series of real numbers
Contextualizes subtle, commonly-misunderstood topics such as the notion of an infinite limit, the ε-δ definitions (for a better command of uniform versus pointwise continuity), error in local linear approximations, and integrability criteria

Carefully dissects key concepts such as limits of sequence, convergence & divergence of monotone sequences, infinite limits, derivatives, integrals, and series of real numbers
Contextualizes subtle, commonly-misunderstood topics such as the notion of an infinite limit, the ε-δ definitions (for a better command of uniform versus pointwise continuity), error in local linear approximations, and integrability criteria
Includes more than 120 exercises, with a solution manual available to instructors

Videos on a first course in calculus (Differential Calculus).