CalcRef reference
Calculus topics
CalcRef groups all 136 of its calculus formulas into 8 topics, from limits and derivatives to integrals, series and polar coordinates. Each topic page lists its formulas with notation, conditions and a link to a worked example, for students revising a course or an exam. Every page here is free to read, with no account needed.
Limits & Continuity
Limit definitions, laws, special limits, and continuity theorems
18 formulas
Derivatives
Derivative rules for polynomials, trig, exponential, and inverse functions
24 formulas
Applications of Derivatives
Tangent lines, optimization, related rates, and curve sketching
15 formulas
Integrals
Fundamental theorem, antiderivatives, and integral properties
19 formulas
Techniques of Integration
Substitution, parts, trig sub, partial fractions, and improper integrals
16 formulas
Applications of Integrals
Area, volume, arc length, surface area, and work
14 formulas
Sequences & Series
Convergence tests, power series, Taylor and Maclaurin series
18 formulas
Parametric, Polar & Vectors
Parametric curves, polar coordinates, and vector operations
12 formulas
Related guides
Prefer to read a topic end to end? These free guides walk through the reasoning behind the formulas above.
Understanding Limits Intuitively: What Calculus Actually Means by "Approaching"
A plain-English guide to limits: what "approaching a value" really means, why 0/0 is not the end of the story, and where one-sided limits and infinity fit.
Every Derivative Rule, in the Order You Actually Learn Them
The derivative rules in the order you learn them: power, constant, sum, product, quotient and chain rules, each with when-to-use guidance.
How to Know Which Integration Technique to Use
When to use u-substitution, integration by parts, trig substitution or partial fractions, with the tell-tale signs that point to each method.
A Realistic Study Plan for Surviving Calculus 1
A week-by-week plan for passing Calculus 1: what to master in each unit, how to practice efficiently, and where students most often fall behind.