# 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 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.

# 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).

# 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!

# 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

# 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.

• 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.

# ODEs for Engineers: Prep Session Tuesday Night

McGill MATH 263 Ordinary Differential Equations for Engineers students come join us Tuesday night for a systematic and comprehensive review of the material that will be covered on your second quiz. Full details below. Register at this link or under the MATH 263 tab, above.

• Quiz 2 Prep:
• Theory: Abel’s Theorem & the Wronskian. Second-Order, Linear ODEs (Fundamental Sets of Solutions; General Solutions).
• Homogenous Equations: Constant Coefficients with Distinct, Complex and Repeated Roots); Reduction of Order.
• Non-Homogenous Equations: Undetermined Coefficients & Variation of Parameters.
• Higher-Order Equations (same content as for second-order ODEs)
• Series Solutions (& basic manipulation of power series).

The session will run Tuesday evening October 28th, 2014 from 8:30-11pm and will place an emphasis on solving problems and applying the theory. The cost will be \$50 for the 2.5h, including notes. RSVP here.

### First Timer’s Discount!

If this is your first time attending one of our sessions, save 40% on the quiz prep session and only pay \$30.