Calculus 1 & 2 Formulas

Smoothness of functions

Operations of functions

Inverse functions

Monotonic properties

Symmetric property

Limit

Continuity

the limit must equal the function's value

Derivatives

Monotonicity and extrema

Mean Value Theorem

Integrals and their properties

Integration by Net Change

Integration by parts

Applications of integrals

Trigonometric substitution

Tangent half-angle substitution

Separable differential equations

First-order linear differential equations

Second-order homogeneous linear differential equations

Second-order non-homogeneous linear differential equations

Probability

Sequences

Series

The Integral Test and Estimates of Sums

The Comparison Tests

The Alternating Series

Absolute convergence

The Ratio Test

The Root Test

Power Series

Taylor and Maclaurin Series

Three-Dimensional Coordinate Systems

Vectors

The Dot Product

Projections

The Cross Product

Equations of Lines and Planes

Vector Functions and Space Curves

Derivatives and Integrals of Vector Functions

Arc Length and Curvature

Functions of Severable Variables

Limits and Continuity

Partial Derivatives

Tangent Planes and Linear Approximations

The Chain Rule

Double Integrals over Rectangles

Double Integrals over General Regions

Double Integrals in Polar Coordinates

Surface Area

Triple Integrals

Triple Integrals in Cylindrical Coordinates

Triple Integrals in Spherical Coordinates

Change of Variables in Multiple Integrals

Vector Fields

Line Integrals

Conservative Test

Green’s Theorem