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Math 213
Analytic Geometry/Calculus III

Classroom: 131 Planetary Hall, MW 1:30-2:45pm

Professor: Anton Lukyanenko, alukyane@gmu.edu
Office Hours: MW 3-4pm, and by appointment, in 4113 Exploratory

TA: Heath Camphire
Office Hours: W 4-6pm, and by appointment, in 4311 Exploratory (or nearby)


Course Description

Differentiation and integration are key tools in many fields, from physics to economics and data science. Calculus 1 and 2 covered the 1-dimensional version of these topics, but most real-world problems are not 1-dimensional. In this course, we will see how calculus works when many dimensions are involved, focusing on the 2D and 3D examples. Making calculus work in multiple dimensions will require us to first review the geometry of 2D and 3D space, and then upgrade the notions of continuity, derivatives and integrals to involve multiple variables. In some cases, we will end up with multiple generalizations (for example, multiplication can be generalized as both the dot product and the cross product).

Since we will be generalizing the content of Calculus 1 and 2 to higher dimensions, the course requires a thorough understanding of both 1D calculus and geometry. Recommended prerequisites are a B or better in calculus 1 and 2, and some time reviewing trigonometry and geometry over the summer.

Want more math? This course will be the "driver's ed" version of Calculus III: we will learn how to use the tools, but won't have time to really understand why they work. If you get excited about the nuts and bolts of mathematics, the details of Math213 are covered in the higher-level Math316. In the meantime, I encourage you to sign up for Math175, "Mathematics of Cryptography: An Introduction", which is a 20-person class specifically for enthusiastic students curious about in-depth mathematics.