Advanced calculus of several variables

This course could be called Advanced Calculus for the Real World, which has at least three dimensions. The prerequisites are Math 4031 (Advanced Calculus I) and Math 2085 (Linear Algebra), or their equivalents. The topics will include properties of Euclidean space, continuous functions, differential calculus in n-dimensional space, the inverse and implicit function theorems, and the Riemann integral in n-dimensions if time permits. This is a theorem-proving course, like Math 4031: Homework will be collected, corrected carefully and returned. The text will be my own set of lecture notes and exercises, which will be available locally at low cost. Math majors with the Mathematics Concentration can complete the advanced calculus component of the upper division requirements with 4031 followed by either 4035 or 4032. The Department recommends but does not require all three courses for students intending to pursue graduate study in mathematics.