# Multivariable Calculus

McGill Math 262 and Math 222, it’s finally your turn – Mastery Sessions start Friday! A super efficient way to review all the material and prepare yourself for the final. Here are the details. Register on the Math 222 or Math 262 pages.

### Mastery 1: – Infinite Series, Vectors & Parametric Functions –

Friday Dec. 12th, 6:30-9:30pm (M3-37A; \$60*): in this three hour session, we’ll review the techniques for finding Taylor, MacLaurin & Power-Series expansions; focusing on representative exam-level practice problems. Come knowing how to handle basic power series & learn the methods and tricks for advanced questions. We’ll also review solutions to standard vector-geometry problems that have appeared on past finals. Finally, the end of the session will focus on the manipulation of parametric functions (integrals; derivatives; arclength; curvature; torsion; radius of curvature T/B/N etc). You should be familiar with the definitions and their basic application. This session is a great way to refresh on the first half of the class in 3h so you can focus on the multivariable content.  *Discounts available, see below for details. Register on the Math 222 or Math 262 pages.

### Mastery 2: Partial Diff, Multivariate Chain Rule, Implicit Diff & Applications

Saturday Dec. 13th, 1:00-4:00pm (M3-37A; \$60*): in this second three hour session, we’ll shift into genuine multivariable mode: looking at exam-level chain-rule and implicit diff questions as well as applications of partial differentiation, including finding tangent planeslinearization; identifying critical points of a multivariate function and classifying the extrema of bivariate functions. As with all mastery sessions, the emphasis will be placed on solving exam-level examples and basic familiarity with the theory is assumed. *Discounts available, see below for details. Register on the Math 222 or Math 262 pages.

### Mastery 3:  Constrained Optimization (Lagrange) and Multiple Integrals

Sunday Dec. 14th, 5-8pm (M3-37A; \$60*): in this third three hour session, we’ll look at exam-level constraint problems requiring the method of Lagrange multipliers, with an emphasis on solving the associated non-linear system of equations (many examples will be provided to help with this process). The rest of the session will focus on multiple integrals requiring iterative methods or change of variable & applications thereof. Emphasis will be placed on advanced exam-level problems. Be sure to know how to compute the Jacobian of a change of coordinates, assuming the substitution is provide. Familiarity with polar coordinates is very helpful. *Discounts available, see below for details. Register on the Math 222 or Math 262 pages.

### Mastery 4:  Full Review – Mock Exam

Monday Dec. 15th, 4-7pm (M3-37A; \$60): This last session will attempt to recreate some of the stress of the exam by presenting you with a mock final in an exam-like setting. Some of the stress of your exam will be approximated by providing an insufficient amount of time to solve the questions, where your goal will be to identify the correct method and setup the appropriate equations and/or anticipate the general form of the solution; we will then solve the questions together. Questions will not be grouped by theory nor content, but will reflect the realistic structure of the exam. Additional variations on each question may be provided, where needed, to help you practice sections that proved most challenging.  *Discounts available, see below for details. Register on the Math 222 or Math 262 pages.

## Discounts:

It’s simple: the more review you get, the better you’ll do, so for every additional session you register for, the deal gets better:

• 1 session: \$60 for 3h, i.e. \$20/h – including notes and practice problems;
• 2 sessions: \$120 \$110 for 6h, i.e. \$18/h – including notes (for each session);
• 3 sessions: \$180 \$150 for 9h, i.e. \$16.5/h (!)- including notes (for each session);
• 4 sessions: \$240 \$180 for 12h, i.e. \$15/h (!!) – including notes (for each session).

Discounts will be applied automatically, additional details and information will be provided in the confirmation email you receive upon registration. Register on the Math 222 or Math 262 pages.