This class is a broad survey of mathematical theories and techniques which are applied in the physical sciences and engineering, but also are of interest in their own right. The class will cover fundamentals of ordinary and partial differential equations, fundamental to classical mechanics, electrodynamics, quantum mechanics, and chemistry. A large part of the course will cover Fourier analysis, which is deeply connected to the solution of partial differential equations, but also of interest in many other applications. The class will also touch on topics such as asymptotics, calculus of variations, and complex analysis.

Note that in our non-standard calculus sequence, we do not cover some standard computational techniques of calculus in the introductory course MAT 4288 Calculus: A Classical Approach. Some of those techniques will be covered in this class instead. Therefore, this class can be a good choice for students who took Calculus: A Classical Approach and want to go further with calculus.

**Learning Outcomes:**

- Develop and practice computational techniques of calculus, particularly integration rules

- Compute Fourier series

- Solve linear partial differential equations by separation of variables, including wave and heat equation

- Connect linear algebra and analysis; understand key ideas in Hilbert spaces

- Continue to develop higher-order conceptual thinking in mathematics ("mathematical maturity")

**Delivery Method: Fully in-person**

Prerequisites: Calculus: A Classical Approach, or any other college-level calculus (by permission of instructor). Linear Algebra also recommended, but not required. Contact Andrew McIntyre by email (amcintyre@bennington.edu), before 4000 registration opens, to be added to the class.

Course Level: 4000-level

Credits: 4

T/F 2:10PM - 4:00PM (Full-term)

Maximum Enrollment: 20

Course Frequency: Every 2-3 years

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

Tags: electrodynamics , physics , quantum mechanics