Calculus textbook (PDF, 250 pages)

Full calculus text book in PDF format. Serves as an introduction to calculus, with clear explanations and plenty of illustrations. Covers functions, limits, differentiation, and integration, including theroems, examples, proofs, and advanced techniques. Suitable for A Level through to introductory undergraduate level.

The PDF file is 250 pages and can be read on screen, or printed out in full or in parts. 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.