Knowledge of Geometries

## "Candidates use spatial visualization and geometric modeling to explore and analyze geometric shapes, structures, and their properties."

### Reflection on the Standard:

One of the courses I have taken to fulfill this standard is Multivariate Calculus. This course covered analytic geometry of functions of several variables, limits and partial derivatives, multiple and iterated integrals, non-rectangular coordinates, change of variables, line and surface integrals, and both Green and Stokes theorems. In this course I gained a conceptual understanding of core concepts and principles of Euclidean and non-Euclidean geometries in both two and three dimensions (meeting indicator 11.1), learned about the role of axiomatic systems and proofs in geometry (meeting indicator 11.2), analyzed the characteristics and relationships of geometric shapes (meeting indicator 11.3), built and manipulated representations of two- and three-dimensional objects (meeting indicator 11.4), described spatial relationships using coordinate geometry, vectors, and parametric, polar, cylindrical, and spherical coordinates (meeting indicator 11.5), and used models, drawings, and geometric software, especially Maple, to explore geometric ideas (meeting indicator 11.7).

### Artifact:

To illustrate this standard, I have selected an exam from Multivariate Calculus. Please click the artifact icon below to view this exam: ### Explanation of Artifact in Relation to the Standard:

On this I exam demonstrated my knowledge of core concepts and principles of Euclidean geometries in two and three dimensions by integrating various geometric regions (meeting indicator 11.1), exhibited my knowledge of the role of axiomatic systems and proofs in geometry by proving that the directional derivative of a function occurs in the direction of the function's gradient, built and manipulated representations of three-dimensional objects by rewriting a triple integral as an iterated integral (meeting indicator 11.4), described various spatial relationships using coordinate geometry (meeting indicator 11.5), and used drawings and Maple to explore geometric ideas (meeting indicator 11.7).

page revision: 7, last edited: 08 May 2009 02:01
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