Registration is now open for the Math 141 Final Exam Mastery Prep sessions: early-bird pricing is open to weekly members first, but non-weekly members can RSVP and will be assigned spots based on availability (first come, first served). Additional sessions *may* be scheduled if there is sufficient interest. Register now on the Math 141 page or by visiting Math141.com. Best of luck with the last weeks of classes!

# Tutor

# Winter 2017: Math 123, Math 133, Math 140, Math 141, Math 222, Math 262, Math 263, Math 314, Math 315 … !

Registration is now open for the following courses for the Winter 2017 semester:

- Math 123 Linear Algebra & Probability (for Management)
- Math 140 Calculus 1
- Math 141 Calculus 2

& you can register for weekly mastery lectures and other sessions directly on their respective course page now!

Registration for the following courses will be open by midweek or sooner:

- Math 133
- Math 222
- Math 262
- Math 263
- Math 264
- Math 314
- Math 315

with updates (here) following soon. If you’re interested in these classes & would like to be kept up-to-speed on weekly mastery lectures, webwork sessions, midterm prep etc. Simply fill out the registration form on the respective course page.

Whether you just want to be more efficient in your studying; want to get an extra edge on the material; improve your intuitive understanding of the course content or need a bit of help sorting out the concepts and preparing for quizzes and exams – I look forward to meeting students of all types at the beginning of every semester & hope you’ll join us – I’m sure you’ll be glad you did!

Wishing you tons of success in 2017!

- Jacob B.

# Final Exam Mastery Prep for McGill Math Classes

… are on their way! Registration is now open for the Math 133 Linear Algebra and Geometry Final Exam Prep Sessions, as well as Math 122 Calculus for Management. See the Math 133 and Math 122 pages, respectively, to register: spots are limited, so register right away to guarantee your spot – you’ll be glad you did!

Registration for Math 139, Math 140, Math 263 and Math 315 will be up in the next couple days, followed shortly thereafter by Math 222 and Math 262 – so check back soon if you’re counting on joining us for those sessions!

# Winter 2016 Sessions

Welcome back!

Only a few days into the winter semester, but things get moving quickly, don’t they?

I’m launching a new site with improved registration interface, over the next month. In the meantime, individual course pages will be updated for temporary use over the course of the week of Jan. 11th.

That being said, I will be running weekly Mastery Lectures for all the usual courses, so if you are interested and would like to register immediately, feel free to use the forms that are currently posted (even if they have not been updated for 2016). If there is no “weekly Mastery Lecture” option, simply leave a comment to let me know.

I’ve also created FB group pages for most of the weekly Lectures. As usual, each group will be launched once we have 9 committed members, so be sure to tell your friends and classmates about the sessions – they will thank you. You can also get in touch with me to help spread the word: with your help, we can get started early and avoid cramming for midterms or assignments etc.

Very much looking forward to working with you all (again!) and trying out some new ideas for helping you understand and succeed!

Best wishes for 2016,

Jacob

# Math 139 Quiz 3

### Math 139 Homepage & Registration Form

This ~2.5h session will cover everything you need to know to ace your third quiz. The focus will be entirely on solving representative quiz-level problems. We will briefly review the necessary theory in an easy-to-understand way, and then see how it applies to the types of questions you can expect to see on your quiz. Despite the brief summaries of the theory, it is expected that students come prepared and with a basic familiarity with the material – the focus will be on probelm-solving.

Topics covered will include: infinite limits; asymptotes; limit-definition of the derivative; rules for differentiation; advanced application of product, chain and quotient rules; implicit differentation; tangent lines; horizontal tangency; application to position, velocity and acceleration, as well as special limits. Click here to go to the Math139.com registration page.

**Cost**: $25 for non-weekly members who register before 9pm Friday; $30 before 5pm Saturday; $35 afterwards, or without a deposit, or at the door (pending space); $20 for weekly members (before Friday 9pm).

**Special offer**: attend the Quiz 3 Mastery Prep Session + Math 139 Mastery Lecture #7 (advanced differentiation: product & chain rule and the general exponential function) for only $45 (for registration before 5pm Friday), $40 afterwards – **limited to 4 spots**.

**Deposit**: to confirm their spot, non-weekly members are required to make a 50% non-refundable deposit. This allows us to guarantee a small group setting where students are able to participate and ask questions.

Deposits can be sent by PayPal or e-transfer to Jacob.Beaudry@mail.mcgill.ca. Via PayPal, please include in the note that it is a non-refundable deposit. Via e-transfer, make the question “Calculus Quiz 3” and the answer “math139” (all lower case, no spaces). Payment can also be made in person between 1-5pm in M3-37A on Saturday.

# Math 262 Written A2 Workshop

**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 141: Quiz 2 Prep

**UPDATE: Additional Quiz 2 Prep Session on Sunday 11am-1pm. **Due to high interest, a repeat of the quiz 2 prep session has been scheduled for Sunday 11am-1pm. Looking forward to seeing you there!

McGill Math 141, Cal 2 – it’s that time again. Quiz 2 is coming up next week & covers a lot more topics that quiz one. So if you need help with substitutions; integration by-parts, combinations of the two; trig-integrals or volumes of revolution, or just want to get that extra edge on the material so you can ace the quiz, then this is the place to start.

### Quiz #2 Prep Session

**Saturday Feb. 14th, 5:00-7:00pm (M3-37A; $25/$20*)**: this 2h session will whip through the concepts and theory included in the second 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): substitution; by-parts (and combinations of both); trig-integrals & volumes of revolution. Acing quizzes right from the start is an easy way to take off some of the pressure on the final exam. Space is limited and sessions are usually full within 12h of posting. *$25 for non-weekly members; $20 for fully-paid weekly members.

### Math 141 Weekly Tutorial #6: Trig Integrals & Trig-Subs

**Sunday Feb. 15th, 3-5pm (M3-37A): **This will be yet another awesome session covering the concepts and theory associated with the intimidating topic of trigonometric integrals *and* integration via trigonometric-substitution. A clear breakdown of the trig integrals will drastically simplify all those integrals that seem unrelated, & my own unique method of identifying and executing trig subs will actually have you looking forward to these questions on the quiz & final exam! As a **special promotion:** register for both the weekly tutorial and the quiz prep for only $40.

# 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 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.