Calculus: Functions and limits, squeeze theorem, differentiation, L'Hopital's rule, integration, Riemann sums, chain rule

This book is an introduction to calculus, mainly concerned with real-valued functions of a single variable.

The book assumes high school maths (UK KS4), and is suitable as an introduction to calculus at undergraduate level or for anyone with a general interest in mathematics.

It covers:

Functions and limits, including domains and codomains, concepts of smoothness and continuity, tangents and slope, and squeeze theorem.
Differentiation, including rates of change, differentiation from first principles, standard derivatives, stationary points, and L'Hopital's rule.
Integration, including indefinite and definite integrals, standard integrals, Riemann sums, the fundamental theorem of calculus, and improper integrals.
Differentiation techniques, including the product rule, chain rule, quotient rule, reciprocal rule, inverse function rule, implicit differentiation and logarithmic differentiation.
Integration techniques, including integration by substitution, integration by parts and the LIATE rule, trig identities, trig substitution, and partial fractions.
The book takes the approach of providing intuitive explanations and examples followed by formal proofs that build on an intuitive understanding.