MATH 2X03, Fall 2018
ADVANCED CALCULUS I
In this course we will study vector fields, their derivatives and integrals. A vector field in a region of R^3 is an assignment of a vector at each point of the region. Good examples to bear in mind are the wind velocity (direction and speed) at each point of the atmosphere, and the gravitational force field between planets. We will explore concepts such as the amount of work done in moving an object along a path through the vector field and the amount of fluid moving across a membrane per unit area per unit time. Mathematically speaking, we will learn how to integrate vector fields. Tying these concepts together are Stokes's theorem and Gauss's divergence theorem, which are generalizations of the fundamental theorem of calculus from the one variable to the vector fields setting. Suitable applications will be presented in the course at appropriate points. The material covered in this course is essential for studying differential geometry (3B03), partial differential equations (3FF3), calculus on manifolds (4B03), complex analysis (3X03), as well as electromagnetism, fluid dynamics, and many other topics in physics and engineering.
Multiple integration, line and surface integrals and applications. The classical integration theorems of Green, Gauss and Stokes.
Three lectures, one tutorial; one term
Prerequisite(s): One of MATH 1AA3, 1LT3, 1XX3, 1ZB3, 1ZZ5, ARTSSCI 1D06 A/B, ISCI 1A24 A/B; and credit or registration in one of MATH 1B03, 1ZC3
Not open to students with credit or registration in ISCI 2A18 A/B.
Not open to students with credit in MATH 2A03, 2M06, 2MM3, 2Q04, 2ZZ3.
PLEASE REFER TO MOSAIC FOR THE MOST UP-TO-DATE INFORMATION ON TIMES AND ROOMS