Offered every fall, winter and spring term.
Brief description:
The first part of the course introduces the concepts and main results of vector integral calculus: vector fields, line and surface integrals and the three famous theorems - Green's theorem, Gauss' Divergence theorem and Stokes' theorem. The second part of the course deals with Fourier analysis, that is, the remarkable idea that a variety of complicated functions can be synthesized from pure sine and cosine functions. Applications to physics and engineering are emphasized throughout the course.
Prerequisite:
MATH 237/247 Calculus 3
Intended audience:
- AMATH 231 is the culmination of the traditional Calculus sequence and will appeal to students who enjoy Calculus and/or are interested in theoretical physics.
- AM 231 leads to continuum mechanics (AMATH 361) - the basis for fluid mechanics, elasticity and biomechanics, with current applications to geophysics, the environment and medicine.
- AM 231 leads to partial differential equations (AMATH 353) - of interest in such diverse areas as fluid dynamics (AMATH 463), Quantum Mechanics (AMATH 373) and the mathematics of finance.
- The introduction to Fourier series and the Fourier transform in AMATH 231 will provide the background for the so-called fast Fourier transform algorithm that arises in numerical computation (e.g. CS 370, AMATH 242), and in digital signal analysis (e.g. ECE 412).