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\title{Mathematics 13 -- Term Syllabus\\\vskip -.1in{\normalsize(Section numbers from Marsden, Tromba, Weinstein)}\vskip -.2in}
\author{The Undergraduate Program Committee}
\date{\today}

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\hline
\textbf{Lecture}
&\textbf{Topics}
&\textbf{Some Standard Examples/Concepts}
\\ \hline
\lecture
&Review of algebra and geometry in Euclidean space (1.1 - 1.5)
&Vector notation, dot and cross products, lines, planes
\\ \hline
\lecture
&Curves in Euclidean space (1.6)
&Curves, tangent vector, tangent line
\\ \hline
\lecture
&Graphs, level surfaces, partial derivatives, and continuity (2.1 - 2.2)
&
\\ \hline
\lecture
&Differentiability, the derivative matrix, tangent planes (2.3)
&
\\ \hline
\lecture
&The Chain Rule, Gradients and Directional Derivatives (2.4 - 2.5)
&
\\ \hline
\lecture
&Directional Derivatives and Implicit differentiation (2.5 - 2.6)
&
\\ \hline
\lecture
&Curves and acceleration (4.1)
&
\\ \hline
\lecture
&Arclength (4.2)
&
\\ \hline
\lecture
&Vector Fields (4.3)
&
\\ \hline
\lecture
&Divergence and Curl (4.4)
&
\\ \hline
\lecture
&Divergence and Curl (4.4 / 5.1)
&
\\ \hline
\lecture
&Volume and Cavalieri's Principle (5.1)
&
\\ \hline
\lecture
&Double integral over a rectangle (5.2 / 5.3)
&
\\ \hline
\lecture
&Double Integral over other regions (5.3)
&
\\ \hline
\lecture
&Triple Integrals (5.4)
&
\\ \hline
\lecture
&Change of Variables, cylindrical and spherical coordinates (5.5)
&
\\ \hline
\lecture
&Change of Variables, cylindrical and spherical coordinates (5.5)
&
\\ \hline
\lecture
&Applications (5.6)
&Center of Mass, moments of inertia
\\ \hline
\lecture
&Line Integrals (6.1)
&
\\ \hline
\lecture
&Line Integrals (6.1)
&
\\ \hline
\lecture
&Parametrized surfaces (6.2)
&
\\ \hline
\lecture
&Area of a surface (6.3)
&
\\ \hline
\lecture
&Surface Integrals (6.4)
&
\\ \hline
\lecture
&Green's theorem (7.1)
&
\\ \hline
\lecture
&Stokes' Theorem (7.2)
&
\\ \hline
\lecture
&Stokes' Theorem (7.2)
&
\\ \hline
\lecture
&Gauss' theorem (7.3)
&
\\ \hline
\lecture
&Path Independence and the Fundamental Theorem of Calculus (7.4)
&
\\ \hline

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