This is a tentative syllabus. This page
will be updated irregularly.
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The geometry of Euclidean space |
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The geometry of real-valued functions
Limits and continuity |
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Differentiation, Introduction to paths,
Properties of the derivative |
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Gradients and directional derivatives.
Iterated partial derivatives. |
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Taylor's theorem.
Extrema of real-valued functions |
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Constrained extrema and Lagrange multipliers.
The implicit function theorem |
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Some applications |
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Acceleration and Newton's Second Law
Arc Length |
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Martin Luther
King Jr. Day |
Classes moved to the X-hour |
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Vector fields
Divergence and curl |
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The double integral |
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The double integral over more general regions
Changing the order of integration |
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The triple integral |
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The geometry of maps from R^2 to R^2
The change of variables theorem |
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The change of variables theorem
Applications of double and triple integrals |
X-period Tuesday Feb 5, 2002 | 6.3, 6.4 | Applications of double and triple integrals
Improper integrals |
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The path integral
The line integral |
Friday - Feb 8, 2002 | Carnival Holiday | Classes moved to the X-period |
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Parametrized surfaces |
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Area of a surface |
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Integrals of scalar functions over surfaces |
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Surface integrals of vector functions |
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Green's theorem |
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Stoke's theorem |
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Conservative fields |
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Gauss' theorem |
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Applications to physics, engineering, and differential equations |
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Differential forms |
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Review |
Last updated: January 1, 2002