This section briefly summarizes the key concepts multivariable calculus students should be learning as they engage with the activities. This section does not replace the courses text, but instead is kept as concise as possible while emphasizing the following for each concept:

\begin{enumerate}

\item quantitative reasoning

\item geometry and geometric relationships

\item multiple representations and their connections

\end{enumerate}

Many relationships in multivariable calculus can be studied independent of a given coordinate system, with the familiar formulas occurring once a particular coordinate system is chosen. In the sections that follow, the concept is first illustrated using a diagram designed to uncover the concept's underlying geometric features. This geometric viewpoint is key; the subsequent formulas are included not to provide a final result but instead to illustrate how the geometric relationships could appear once written down algebraically within a coordinate system.

Topics include:

\begin{itemize}

\item Notation Conventions

\item Coordinate Systems

\item Geometry of the Dot Product

\item Geometry of Partial Derivatives

\item Geometry of Gradient Vectors

\item Geometry of Directional Derivative Vectors

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*Geometric Conditions for Constrained Optimization - Lagrange Multipliers* does not exist.

\item Geometric Conditions for Optimization with a Bounded Domain

\item Geometry of Tangent Vectors

\item Integration as Accumulation instead of Area under a Curve

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*Geometric Representation of Scalar ds Integrals* does not exist.

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*Geometry Cross Product* does not exist.

\item Geometric Representation of Surface Area

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*Geometric Representation of Scalar dV Integrals* does not exist.

\end{itemize}

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*geometry-behind/level-curves* does not exist.