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.

**Learning Outcomes:**

- Students will learn to employ the fundamental concepts of multivariable calculus

- Students will learn to identify applied problems to which multivariable calculus applies, and to formulate the problems appropriately

- Students will generally develop greater sophistication and integration of topics within mathematics (particularly calculus and linear algebra)

**Delivery Method: Fully in-person**

**Prerequisites:**

Linear Algebra, and Introductory Calculus (either at Bennington College or elsewhere). Permission of instructor required. Contact Andrew McIntyre (amcintyre@bennington.edu) by email to ask questions and to register.

Course Level: 4000-level

Credits: 4

T/F 4:10PM - 6:00PM (Full-term)

Maximum Enrollment: 20

Course Frequency: Every 2-3 years

Categories: 4000 , All courses , Four Credit , Fully In-Person , Mathematics

Tags: artificial intelligence , economics , geometry , machine learning