Happy New Year & welcome back for part 2 of the academic grind! I’m currently updating the site & info for all classes, but you needn’t wait for your page to be updated in order to register, just get in touch using one of the contact forms or email me directly if you’re keen to get started soon. The first groups will be up and running this weekend and I expect all classes will be running by the following weekend. Looking forward to another great term working with you all! Stay warm!

# Author: mcgillcalhelp

# 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 263 – Final Exam Review

As promised, registration for McGill Math 263 ODEs for Engineers is now open. Full details below; register here. NB. the following outlines are approximate and tentative and subject to review and requests from participants; check the Math 263 page for updates.

### Mastery 1: Methods for 1st and 2nd Order Linear ODEs

**Thursday Dec. 4th, 4:45-7:45pm (M3-37A; $60*): **in this three hour session, we’ll review the techniques for solving first and second order ODEs, focusing on representative practice problems. Topics will include: integrating factors; separable equations; autonomous equations; exact equations; exact equations requiring an integrating factor; the method of undetermined coefficients; the method of variation of parameters. This will include a very quick overview of the three types of 2nd order, constant-coefficient DEs, but basic familiarity will be assumed so that we can focus on advanced applications of the less familiar topics. More information will be provided upon registration. *Discounts available, see here for details.

### Mastery 2: Euler, Series, Frobenius & Bessel

**Sunday Dec. 7th, 7:15-10:15pm (M3-37A; $60*)**: in this second three hour session, we’ll continue the review of the various methods for solving DEs with further examples applied to non-homogenous equations, and special focus on their application to higher-order DEs. The rest of the session will look at the series solution of the general, homogenous, 2nd order DE about ordinary points; general Euler equations and Frobenius series solutions about regular singular points. Familiarity with the 3 basic cases for Euler’s equations will be assumed and additional preparation will be recommended to help you get the most out of the session. *Discounts available, see here for details.

### Mastery 3: Laplace & Systems of Equations (all types)

**Wednesday Dec. 10th, 6-9pm (M3-37A; $60*): **in this third three hour session, we’ll look at exam-level Laplace Transform problems with special emphasis on finding transforms and their inverses (although we will also solve a few advanced IVPs to illustrate the complete method), including step functions, discontinuous forcing functions, impulse functions, the convolution of two functions and combinations thereof. Finally, the balance of the session will focus on the solution of linear systems of DEs and all cases with which you should be familiar for the exam (exact details will be provide upon registration). *Discounts available, see here for details.

### Mastery 4: Mock Exam

**Thursday Dec. 11th, 1-4pm (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 or content, but will reflect the realistic structure of the exam. Additional variations on each question will be provided to help you practice sections that proved most challenging. *Discounts available, see here for details.

# Mastery Sessions Registration

They’re here! Mastery Sessions for McGill Math 139 final exam prep; McGill Math 140 final exam prep and McGill Math 141 final exam prep. Everything you need to understand and succeed on your final. Space is limited and sessions usually fill up within ~72h of registration opening. Full details and registration at the links provided. Details for Math 263, 222 and 262 coming soon. Best of luck with the end of term!

# 139 Quiz 4

### McGill Math 139 Quiz 4 Prep:

#### Update: the session is now full & registration has been closed.

This Thursday we’ll meet for ~2h (starting at 7pm) to run through a ton of problems to prep you for the last quiz. Space is limited and registration is first-come, first-served. The session will be $25 if you RSVP, $30 at the door (though I don’t expect there will be room).

# McGill Math 122 Calculus for Management Fall 2014 Final

They’re here: the best final review & prep sessions for MATH 122 Calculus for Management Students at McGill! **We don’t run a “crash course” aimed at helping you just scrape by, we run mastery sessions that assume you’re familiar with the basics, and so aim to help you understand the subtleties that come up in advanced, exam-level applications so you can understand and succeed.** Space is limited, registration is first-come, first-served. Additional dates will be added if there is sufficient interest. See below for descriptions of each of the sessions and information about available discounts.

### Mastery 1: Tuesday Nov. 25th, 6-9pm ($60*)

In this three hour session, we’ll review the application of derivatives to consumer and producer surplus; the optimization of various systems modelled using a single variable; related rates of time-dependent systems, linear-approximation, and the basics of curve-sketching. Each of these sections has a few fairly representative types of problems which, if mastered, will prepare you for related material on your final. Additional practice problems will be provided so that you can get lots of practice with these types of questions well before the exam. *Discounts available, see below for details.

### Mastery 2: Friday Nov. 28th, 5:30-8:30pm ($60*)

In this second three hour session, we’ll look at exam-level questions requiring implicit differentiation (tangent lines; second derivatives, and in combination with related rates). We’ll also practice dealing with advanced derivatives (logarithmic differentiation; general-exponential differentiation; advanced chain-rule with product rule etc); the limit-definition of the derivative; limits themselves – especially as applied to full curve-sketching questions. Additional practice problems, representative of exam-level material will be provided for additional practice. *Discounts available, see below for details.

### Mastery 3: Friday Dec. 5th, 5:30-8:30pm ($60*)

In this third three hour session, we’ll take your integration skills to the next level; helping you identify the correct method of integration and how to approach every integral systematically. Then, we’ll look a large sampling of exam-level improper integrals, including a list of ”classic” questions that you should know how to solve. Finally, we’ll solve some advanced area & volume-of-revolution questions. As with all the other sessions, additional practice problems will be provided. *Discounts available, see below for details.

### Mastery 4: Saturday Dec. 6th, 4:30-7:30pm ($60*)

This last session will attempt to recreate some of the stress you experience during the exam by limiting the amount of time you have to solve challenging questions from all the topics of the class, presented as they would be in your exam. Emphasis will be placed on efficient strategies, pattern recognition and identifying your weakest points so that you can focus your studying most effectively in the last days before your final. The session will follow the form of a past final and variations on those problems will be provided for additional practice. *Discounts available, see below for details.

### Discounts:

It’s simple: the more review you get, the better you’ll do, so for every additional session you register for, you save $10:

- 1 session: $60 for 3h, including notes and practice problems;
- 2 sessions: $110 for 6h, including notes and practice problems (for each session);
- 3 sessions: $160 for 9h, including notes and practice problems (for each session);
- 4 sessions: $210 for 12h, including notes and practice problems (for each session).

Discounts will be applied automatically, additional details and information will be provided in the confirmation email you receive upon registration.

# MATH 263 Webwork Session

**McGill MATH 263 Ordinary Differential Equations for Engineers – don’t let webwork get you down.** This **Thursday Nov. 13th from 6-8pm we’ll whip through your webwork assignment so you can finish well before midnight**. We also have a weekly MATH 263 tutorial on Saturdays from 2:30-4:30pm where we cover all the theory you need to know to ace the exam, in an easy-to-understand way. **Special promotion:** register for your first weekly MATH 263 tutorial at the same time as the Webwork Session and save $5!

**Need help with MATH 262 Assignment 3 as well? Sign up for both sessions & save $5 off each!**

# MATH 139 Quiz 3 Review

McGill Math 139 Quiz 3 prep this Thursday: two hours dedicated to solving lots of problems from the (numerous!) sections covered recently. We’ll be following the outline provided by your professor very closely. Only $20 for the 2h, register below – don’t hesitate to get in touch if you have any questions!

# MATH 222 – Assignment 3

# A workshop for the cal 3 written assignment

McGill MATH 222 Cal 3 students: an assignment due 2 nights after the midterm?! They must really love you guys :D Thursday night we’ll be running a workshop covering questions exactly parallel to your written assignment: $15 for 1.5h – save yourself the wasted time & unnecessary frustration, it’s really not so bad when properly explained. RSVP using the link below:

**Thursday Nov. 6th, 2014 4:30-6pm in M3-37F; $15 for 1.5h**

# 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**.