Calculus Formulas

Calculus Formulas is a pocket reference for calculus students. Every formula is typeset clearly, explained symbol by symbol and followed by worked examples and practice questions with answers. What's inside • Precalculus essentials: algebra, functions, trigonometry, identities, exponentials and logarithms • Limits and continuity: one-sided limits, limit laws, special limits, asymptotes and the Intermediate Value Theorem • Derivatives: the limit definition, product, quotient and chain rules, implicit and logarithmic differentiation, and a full derivative table • Applications of derivatives: tangent lines, linear approximation, related rates, maxima and minima, the Mean Value Theorem, curve sketching, optimisation, L'Hôpital's rule and Newton's method • Integrals: Riemann sums, the Fundamental Theorem of Calculus, a table of integrals, substitution, integration by parts, trigonometric integrals, trigonometric substitution, partial fractions, improper integrals and numerical integration • Applications of integrals: area between curves, volumes by disks, washers and shells, arc length, surface area, average value, work and centre of mass • Sequences and series: convergence tests, power series, Taylor and Maclaurin series with a table of common series • Parametric equations and polar coordinates: slopes, areas and arc lengths • Multivariable calculus: vectors, partial derivatives, gradient and directional derivatives, extrema and Lagrange multipliers, double and triple integrals • Differential equations: separable and linear equations, growth, decay and logistic models, and second-order linear equations Who it is for Students in AP Calculus and first-year university courses (Calculus I to III), and anyone who wants a quick, reliable reminder of a formula. Features • 57 topic pages in 10 sections • Clear drawings: secant and tangent lines, Riemann sums, area between curves, disk and shell methods, polar graphs, slope fields and more • Worked examples and tap-to-reveal practice questions on every topic • Search across all pages • Works offline, with no account needed • Dark mode • Available in 8 languages: English, Español, Português, Français, Deutsch, العربية, हिन्दी and Bahasa Indonesia Formulas were checked against OpenStax Calculus Volumes 1–3 and the NIST Digital Library of Mathematical Functions. This app is an independent study aid. It is not affiliated with or endorsed by any exam board, textbook publisher or university.