MA330 ‐ Vector Calculus (Fall 2022)

Office Hours

MTRF 3:00-4:00 and by appointment.

Section

MA330-01 — MTRF 2:00-2:50

Course Content

The syllabus, homework, course announcements, and other relevant information will be posted in Moodle. Please check it regularly!

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In MA330 - Vector Calculus (Course Catalog), we will further explore the geometry of curves/surfaces and develop notions of "derivative" and "integral" over vector fields. In particular, considerable effort will be dedicated to applying vector fields to model a variety of phenomena, as well as understanding how to "measure" vector fields both locally (via Divergence and Curl) and globally through the fundamental theorems of integration (i.e. the theorems of Green, Gauss, and Stokes).

This course will not formally require a textbook, though I will likely suggest some books for recommended reading.

In addition to the usual applications to fluid/heat flow and to electricity/magnetism (e.g. Maxwell's Equations), we will use the key ideas and theorems of vector calculus to compute various physical quantities for 2D and 3D models, such as one might construct with vector graphics and/or CAD software:

Model file consisting of many of triangles!
(Source: Thingiverse)

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Vector Calculus! \[ \iiint_E \mathrm{div} \vec{F} \, dV = \subset\!\!\supset\kern-1.65em\iint_{\partial E} \vec{F} \cdot \widehat{n} \, dS \]

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Volume,
Center of Mass,
Moments of Inertia,
and more!

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