Mathematics

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Green's Theorem
Formal Sciences

Green’s Theorem

Green’s Theorem for Simple Connected Regions Theorem. (Green’s Theorem) Let $R$ be a simply connected region with a piecewise smooth boundary curve $C$ oriented counterclockwise

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Line Integrals
Formal Sciences

Line Integrals

Definition of a Line Integral Let $C$ be a smooth curve, with parametric equations $x=x(t),$ $y=y(t),$ and $z=z(t)$ for $a\leq t\leq b,$ that lies within

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Vector Fields
Formal Sciences

Vector Fields and Gradient Fields

Introduction to Vector Fields Definition. A vector field in $\mathbb{R}^n$ is a function $\mathbf{V}$ that assigns a vector from each point in its domain. A

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inner product space
Formal Sciences

Inner Products and Orthonormal Bases

Recall that the norm of $x\in \mathbb{R}^n$ defined by $\left|\left |x\right|\right | = \sqrt{x_1^2+x_2^2}$ is not linear. To injective linearity into the discussion we introduce

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