This would be a good page to bookmark while taking multivariable calculus (MATH2060 at my school). Listed are some useful equations with short descriptions.

Operation	Notation	Description
Del Operator	∇ = a[∂/∂x] + b[∂/∂y] + c[∂/∂z]	Equivalent to gradient operation. Sum of partial derivatives with respect to each basis, multiplied by each basis, multiplied by function (respectively). a, b, and c are basis vectors which are equivalent to <1, 0, 0>, <0, 1, 0>, and <0, 0, 1> in real space.
Gradient	grad(f) = ∇f	Measures change in a scalar field. Maps scalar field domain to vector field.
Curl	curl(F) = ∇xF	Measures the tendency to rotate about a point in a vector field in space. Maps vector field domain to (pseudo)vector field.
Divergence	div(F) = ∇⋅F	Measures scalar of a source or sink at a point in a vector field. Maps vector field domain to scalar field.
Laplacian	∆f = ∇2f = ∇⋅∇f	Measures the difference between the value of a scalar field with its average. Maps scalar field domain to scalar field.
2D Wave Equation	∂2u/∂t2 = c2∇2u or □u = 0	□ = (1/c2)(∂2/∂t2) - ∇2 c is some non-negative real coefficient. u is a scalar field representing displacement from rest in the wave medium (fluid pressure, height of water, etc). Relates displacement from rest with time.
Fourier Transform	ℱ{f(x)} = ∮f(x)⋅e-2πjωxdx	Contour integral means over infinite limits on x. The Fourier Transform is the Laplace Transform with the real part of the complex frequency restricted to 0.

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