Multivariable calculus (advanced)

This unit is an alternative to MTH2010 for students with a strong mathematical foundation.

Students enrolled in MTH2015 will follow the same curriculum as students in MTH2010 and will cover additional more advanced material.

Functions of several variables, partial derivatives, extreme values, Lagrange multipliers. Multiple integrals, line integrals, surface integrals. Vector differential calculus; grad, div and curl. Integral theorems of Gauss and Stokes. Use of a computer algebra package. Curves in 3-space, notions of torsion and curvature. Introductory notions of topology and geometry (stereographic projection). Basic introduction to real analysis: pointwise versus uniform convergence of functions of one variable. Introduction to complex analysis: holomorphic functions, harmonic functions, complex integration, Cauchy's integral formula, the fundamental theorem of Algebra.