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Introduction to calculus, mainly concerned with real-valued functions of a single variable. Based on several articles I have previously published on graphicmaths.com, plus a lot of new material.
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, smoothness and continuity, tangents and slope, squeeze theorem.
- Differentiation, including rates of change, differentiation from first principles, standard derivatives, stationary points, L'Hopital's rule.
- Integration, including indefinite and definite integrals, standard integrals, Riemann sums, fundamental theorem of calculus, improper integrals.
- Differentiation techniques, including the product rule, chain rule, quotient rule, reciprocal rule, inverse function rule, implicit differentiation, logarithmic differentiation.
- Integration techniques, including integration by substitution, integration by parts and the LIATE rule, trig identities, trig substitution, partial fractions.
The book providies intuitive explanations and examples followed by formal proofs that build on an intuitive understanding.