In Section 7.11 we extend the concepts of differential calculus from real valued functions of several variables to vector valued functions of several variables. In Section 7.12 we study the inverse and implicit function theorems for these vector valued functions.

In Section 8.5 we study change of variables in double and triple integrals. Applications are made to polar coordinates, cylindrical coordinates and spherical coordinates.

We study line integrals in Sections 9.2 to 9.5 to generalize the definite integral from real valued functions defined on an interval to real valued and vector valued functions defined on a curve. We derive Green's Theorem to compute the line integral along the boundary of a region D in the plane as a double integral over D. In Sections 9.6 and 9.7 we generalize the double integral from real valued functions defined on a closed region in the plane to real valued and vector valued functions defined on a surface. We derive Stokes' Theorem which generalizes Green's Theorem from flat regions in the plane to surfaces. Then we derive Gauss' Theorem to compute the surface integral over the boundary of a region B in 3 dimensions as a triple integral over B.

The course conlcudes with an introduction to functions of a complex variable. The arithmetic of complex numbers is introduced in Section 5.8. Complex power series are studied in Section 5.9, and they are used to define the exponential, logarithm and trigonometric functions of a complex variable. In Section 7.13 the complex derivative of these functions is defined and studiend. In Section 9.12 contour integrals of these functions are defined. Cauchy's Theorem is derived from Green's Theorem and is applied to prove the Fundamental Theorem of Algebra.

HOMEWORK: You are expected to do all of the assigned homework. Experience has shown that the only way to learn math is to do it - math is not a spectator sport! The amount you learn in this course and the grade you receive will be proportional to the amount of time you spend doing problems.

EXAMS: There will be two in-class exams and a 3 hour final exam. Exams will have short answer questions which test your understanding of the material and long answer questions which test your ability to make computations.

MARKS: The final exam will count as 50% of your mark, and each in-class exam will count as 25% of your mark.

MISSED EXAMS: There will be no make-up exams for missed in-class exams. Upon presentation of documentation of a valid excuse, the corresponding percentage of the final mark will be added to the final exam. With no presentation of such documentation a grade of zero will be entered for the missed exam. If you miss the final exam then it is your responsibility to complete the required paperwork for deferred standing during the first week of January. A make-up final exam for students with deferred standing will be given on the Monday of Reading Week. Any student who receives deferred standing after that date will have to write the final exam with the students of a later course such as the Summer Math 3010 final exam.

IMPORTANT DATES: Add deadline without my permission: Sept. 20.
Add deadline with my permission: Oct. 4.
Drop deadline: November 8.