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Course Description

Summary

Multivariable calculus is one of the core parts of an undergraduate mathematics curriculum. Introductory calculus mostly concentrates on situations where there is one input and one output variable; multivariable extends differentiation, integration, and differential equations to cases where there are multiple input and output variables. In this way, multivariable calculus combines calculus and linear algebra; the subject can also be called vector and matrix calculus. In addition to its fundamental role in mathematics itself (particularly in the study of geometry of surfaces and solids in multiple dimensions), the subject is essential to all sorts of applications, notably in economics, biology, physics (particularly electromagnetism) and computer science (particularly machine learning). This course covers the standard topics in multivariable calculus, including derivatives as linear transformations, Lagrange multipliers, and vector derivatives div, grad, and curl. Note that this class may be taken simultaneously with the introductory class Geometry and Physics, for students who want the tools to take the concepts of Geometry and Physics further. Alternatively, this class may also be taken simultaneously with the advanced class Differential Geometry, Gauge Theories, and Gravity; ideally, students taking the latter class will have taken Multivariable Calculus earlier as a prerequisite, but it is possible to take it as a simultaneous co-requisite instead.