**Math 262 Intermediate Calc for Engineers ****Wednesday Feb. 18th 6:30-8:30pm:** a special session looking at the material from A2 to help you whip through the assignment and really understand the material. $25 for non-weekly members for a 2h session covering the entire assignment; $20 for weekly members. Register below or on the Math 262 page.

# MATH 262

# Math 141: Tutorial, Quiz Prep & WebWork #1

McGill Math 141, Cal 2, this is your week to get things moving! Three sessions to help you recover from the busyness of the start of term, get ready for that first quiz, take care of that first webwork *and* keep up with the material so far! & it’ll be e-z! Full details and registration on the Math 141 page.

### Weekly Tutorial #2: Definite Integrals & the FTC

**Friday Jan. 23rd, 5:30-7:30pm (M3-37A; $35/$40/$50*): **this will be the second of 12 weekly tutorials covering all the theory and concepts from Math 141. We’ll be focusing on evaluating definite integrals and their relationship to FTC, as well as developing you intuitive understanding of the FTC. Detailed notes with fully developed solutions to highly representative practice problems included. *****Registration and full details about pricing options on the Math 141 page.

### Quiz #1 Prep Session

**Saturday Jan. 24th, 1:00-3:00pm (M3-37A; $20/$15*)**: this 2h session will whip through the concepts and theory covered by the first quiz and focus on solving a number of highly representative problems based on quizzes from the previous years (drawing on a bank of >10 years). Acing quizzes right from the start is an easy way to take off some of the pressure on the final exam. Space is limited. *$20 for non-weekly members; $15 for fully-paid weekly members. Register on the Math 141 page.

### WebWork #1 Workshop: No More Tears

**Sunday Jan. 25th, 1-3pm (M3-37A; $20/$15*): **a 2h session that will whip through problems that are structurally identical to your webwork problems, explaining the theory along the way. You won’t need Wolfram or Yahoo to answer your questions after this session. Save yourself the hours of banging your head against the wall & scouring the internet and get your assignment done quickly (while actually understanding it!). *$20 for non-weekly members; $15 for fully-paid weekly members. Register on the Math 141 page.

# 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 planes; linearization; 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.

# McGill MATH 262 & 222 Midterm Prep

# Multivariable Calc: All the Practice You Need*!*

Time to get serious MATH 222 & 262. These sessions will focus on problem-solving at the exam level. It will be assumed that you are familiar with the basics; however, questions will be fully explained so that you are able to apply the concepts to similar problems that are not identical. See below for available discounts.

**Midterm Prep 1 – Mastering Series:**Remember Power Series?! Oh, and MacLaurin Series & Taylor Series? Radii of Convergence; Taylor Coefficients and Approximations. This 3h session will focus on solving tons of midterm-level problems.

**Fri. October 31st, 2014, 5-8pm in M3-37A (3rd floor McLennan); $60 for 3h + notes; discounts available (see below).**

**Midterm Prep 2 – Mastering Vector Geometry:**Lines, Planes & Points, the distances between them all and a look at the (finite!) variations they can give you on these classic questions. These questions can be free points on your midterm!

**Sat. November 1st, 2014, 6:30-8:30pm in M3-37A (3rd floor McLennan); $40 for 2h + notes; discounts available for multiple sessions (see below).**

**Midterm Prep 3 – Mastering Vector-Valued Functions:**Position, Velocity & Acceleration; Arclength and the Arclength Functions; T/N/B, the Frenet Frame, curvature and torsion; Points of Intersection: a whole lot of practice problems!

**Sun. October 26th, 2014, 12:45-2:45pm in M3-37A (3rd floor McLennan); $40 for 2h + detailed notes; discounts available for multiple sessions (see below).**

**Midterm Study Hall 1:**The key to success in this class is*practice*. Study Halls provide an ideal environment for getting that practice without wasting time.

**Sun. November 2nd, 2014, 5:45-8:45pm in M3-17B (3rd floor McLennan); $20 for 3h.**

**Midterm Study Hall 2:**“(Perfect) Practice Makes Perfect” so come work on practice problems with classmates at a midterm-focused Study Hall and have the most challenging questions answered by an experienced tutor.

**Mon. November 3rd, 2014, 5:00-8:00pm in M3-37A (3rd floor McLennan); $20 for 3h.**

**Assignment 3 Workshop (MATH 222):**A session were we’ll look at problems that are structurally identical to those in your assignment: learn everything you need to complete the assignment without spending hours scouring the net & trying to decipher the hieroglyphics of ASCII math, understanding little to nothing. You might be surprised at how easy it actually is!

**TBA,November 2014; $20 for 2h.**

**Best Price Discount:** RSVP for all the midterm sessions and **save ~25%** – take **$10 off** the price of **each prep session** *and* **$5** **off** of **each study hall**; only pay $140 for 13 hours dedicated to helping you understand the material & ace your midterm.

**Multiple Prep Session Discount:** RSVP for more than one prep session and receive **$10 off** the price of *each* session!

**Prep Session + Study Hall Discount:** RSVP for a prep session and a study hall and **save $10**.

# The Multivariable Calculus Study Hall Begins!

McGill MATH 222 and MATH 262 it’s time to get serious about problem solving! **The first Study Hall will be this Thursday October 2nd in room M3-17B** on the third floor of McLennan Library from 5-8pm. The cost is $20. I’ll provide some sample material to work from (past assignments, past midterms etc.). I suggest you focus on material related to sequences and series, power, MacLaurin & Taylor series.** Register for the session** here.

# The *real* new-year: back to it!

Howdy all! Welcome (& welcome back) to the *grind! *We’re only into the third week of classes and already things are moving full *tilt*. Very excited to announce that this year I will be acting as the in-house tutor for the Mastercard Foundation’s scholarship program at McGill: meaning I get to work with the wonderful and talented scholarship students in MATH 133, MATH 139, MATH 140, CHEM 110 and physics, which means all these groups are ready to go. If you’re interested in any of them, just get in touch using the contact form at the bottom of the Tutorials page (under “About”).

In addition to the above classes, we also have groups for MATH 222, MATH 262, MATH 263, and hope to be introducing a class for ISLA 521 – Introductory Arabic. Many of these are quickly reaching capacity, so if you’re interested, be sure to get in touch ASAP. If you’d like to join a group but your class isn’t listed, use the contact form on the Tutorials page and mention your class in the comments field.

Finally, a doodle has been posted for the homework sessions. This will be used to determine potential times for holding homework sessions during the week, so if you’re hoping to attend these often, be sure to fill out your *general, weekly* availability ASAP. The first sessions will be posted here on the site as soon as we have min. 5 people available at the same time.

Looking forward to helping you understand *&*nd succeed in your classes this year. Remember, if you have any questions, just get in touch – I’m here to help!

~ Jacob B.

# MATH 222 & 262, this one’s for you…

Power Series got you down? Maclaurin series threatening you with a zero? Worried Taylor series will leave you with a *c*? Today (Tuesday May 13th) during the second MATH 222 / 262 multivariable session from **1:15-4pm in room M3-37A on the third floor of McLennan Library**, we’ll be telling the story of infinite series & you can be certain you won’t have any trouble remembering the ideas after this session! Here’s an excerpt from the notes:

“Holy smokes, Batman – we can add infinitely many numbers together and their sum may be a finite number!” said Robin. “That’s right my bird-burly buddy! Not only that, but in some special cases, the same series will converge for a range of different values of the constants involved, so we can think of the resulting object as an infinite polynomial” replied his caped companion. “That sure is

ourkind of series, Batman: a realpowerseries! I still can’t believe that such a thing as an infinite polynomial function actually exists . . . it almost seems diabolical. Oh, why here comes Alfred – it looks like he’s got urgent news. What is it Alfred?” chirped the man-bird superhero, inquisitively. “Masters – there’s been a disconcerting development at city hall: when the press release was made that some infinite polynomials are functions, an astute journalist asked the Mayor’s office ‘which functions are involved? any function at all? only polynomials? what about transcendentals? should we be concerned?’ Panic ensued and I think you can expect a call on the bat phone, shortly.” panted the faithful servant.

However don’t be mislead by the above: we’ll be doing plenty of heavy lifting during the session, including a step-by-step overview of how to tackle each of the different types of series problems. Time permitting, we’ll look at estimating errors, review some of the vector content and introduce multiple integration so you can get a head-start on preparing for the final exam.

# May Sessions are Here!

That’s right: we’ve got sessions going for MATH 133, MATH 140, MATH 141, MATH 222 & MATH 262 at the moment. If you’d like join any of these groups, or get a session going for another class, you can register using the form on each class page or send us a note! To everyone who aced their winter exams: congrats & have a great summer!