# 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.

# Calculus For Management: Everything You Need!

With the midterm only a week away, we’re happy to announce details for the MATH 122 Calculus for Management midterm prep sessions.

Best Price Discount: RSVP for all the midterm sessions and save over 25% – take \$10 off the price of every prep session and study hall; only pay \$160 for 17h dedicated to helping you understand & succeed on your midterm, that’s less than \$9.50/h!

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.

# McGill MATH 133 Midterm Prep (2014)

Linear Algebra & Geometry Midterm Prep Session this Monday, October 6th from 4:30-6:30pm in room M3-37A on the third floor of McLennan Library. RSVP using the registration form on the MATH 133 page. Amongst other things, we’ll cover:

• Systems of Linear Equations: solving systems and correctly interpreting the result; working with and moving between different notations.
• Matrix Algebra: definitions and advanced problems from past midterms and finals.
• Row Reduction: learn to find RREF without having fractions everywhere!
• Elementary Matrices: definitions and relationship to the inverse of a matrix.
• Determinants & Inverses of Matrices: direct application and solving of problems.

The session will be \$40 and include notes and practice problems and will definitely help clarify common points of (major) confusion! Some feedback from past students:

#### I just wanted to say thank you again for all your help this semester. I ended up getting an A on the final, which is the best I’ve done in any math course yet. I found the exam really tough, but really understanding the concepts as you taught us instead of just trying to memorize procedures for solving problems really helped me out a lot!

– Aaron Rock MATH 133 Linear Algebra & Geometry Winter 2014

#### I’d just like to let you know that I got 100% on my linear algebra MATH 123 final, and got 100% in the course. I really appreciate your help, I couldn’t have done it without your sessions.

– Trevor Thorburn MATH 123 Linear Algebra & Probability Winter 2014

#### Thanks so much for everything. You are an excellent teacher and I would not have passed without you!

– Erica Vandersteen MATH 133 Linear Algebra & Geometry, Winter 2014

# 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 our kind of series, Batman: a real power series! 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.

# MATH 141 – Final Exam

Final Review Session: Mock Final Based on Prof. Hundemer’s Sample – Friday April 11th, 4:30-7:30pm, M3-37A on the third floor of McLennan. This will be a mock-final based on the sample MATH 141 final provided by Prof. Hundemer. In the fall term, his sample 140 final matched the actual exam very closely both in format and difficulty. As such, I’ve written two exams similar to the sample in those respects, but with different questions. This session will look at the second of these two exams, which is similar in style but more difficult than Prof. Hundemer’s version. Students will have short intervals for attempting the problems followed by a brief discussion of the solution, as a group. \$55 for the session + copies of both exams, \$50 for the session + today’s exam only; \$10 off if you bring a friend. Please RSVP with Adaam at McGill.Calc.Help -at- gmail.com; though drop-ins are welcome. See full details at the MATH 141 page.

Good luck with finals!

# MATH 141 – Integration Session & Final Review

Integration Session: Sunday April 6th 3-5pm, M3-37A on the third floor of McLennan. We’ll be covering 30-50 integrals from past exams. Students will have 30-60s to identify the correct method of integration and any other relevant information, then we’ll discuss the solution briefly as a group. \$5-7 for Mastery Students; \$20 for others. Please RSVP with Adaam at McGill.Calc.Help -at- gmail.com; space is limited. Interested students should be proficient with the basics of each method of integration.

Final Review Session: Tuesday April 8th, 6-9pm, M3-17B on the third floor of McLennan. This will be a mock-final based on the sample final provided by Hundemer. In the fall term, his sample 140 final matched the actual exam very closely both in format and difficulty. As such, I’ll be writing a new exam similar to the sample in those respects, but with different questions. Students will have short intervals for attempting the problems followed by a brief discussion of the solution, as a group. \$40, \$10 off if you bring a friend. Please RSVP with Adaam at McGill.Calc.Help -at- gmail.com. See full details at the MATH 141 page.

Good luck with finals!

# MATH 141 – Crash Course

Panicked about cal 2? Haven’t really started to review yet? No worries – we’ve got you covered :D. We’ll be running a crash-course for MATH 141 starting next Wednesday, April 9th, 2014. The aim of the crash will be to teach you the basics of everything you need to succeed and help you focus your studying most efficiently. The schedule:

• Wednesday April 9th, 7:30-10:30pm – Methods of Integration: learn to integrate any expression. This session includes >100 examples from past exams as well as a complete summary and accessible explanation of each method of integration.
• Thursday April 10th, 7:30-10:30pm – Applications of Integration: areas, volumes, arc-lengths, surface areas, FTC I&II, MVT. Learn to relate all these subjects to each other and reduce the load on your memory – includes simple explanations that will make the material intuitive and accessible.
• Friday April 11th, 7:30-10:30pm – Polar & Parametric Everything: this session will cover everything from basic derivatives and tangent lines to curve-sketching, areas, lengths, surface area & more. We’ll look at tons of questions from past exams and consider strategies for dealing with these questions.
• Saturday April 12th, 3:30-6:30pm – Sequences and Series: discover the easy way to understand sequences and series. We’ll review the tests for convergence and divergence and explain the logic behind them so that you can develop strong intuition about the behaviour of series. You’ll learn to assess the convergence /divergence of most exam-level series at a glance, as well as how to structure a formal solution.

This a small group crash course, which guarantees optimal interaction with the teacher. Sessions are \$80/each or all 4 for \$210, including detailed notes and tons of practice problems. For more information or to register, contact us at mcgill.calc.help -at- gmail.com.

# MATH 141 – Mastery Sessions

The second MATH 141 Mastery Session in preparation for the final exam will be tomorrow, Saturday March 29th from 12:30pm-3:30pm. Mastery 2 – Pre-session Worksheet Be sure to work through the questions and do a quick review of these topics so that you’re familiar with their basic application. As usual, the focus of the session will not be on understanding the ideas at an introductory level; rather, we’ll spend most of our time solving advanced exam-level questions and developing strategies for doing so. See you there!

# MATH 133 – New Group

We’re excited to announce the start of a new weekly group for MATH 133 – Linear Algebra. This is a great class to teach because the material is very conceptual, so a good teacher can make all the difference. We’ll be meeting on Sundays from 12:45-2:45pm. You can register using the form at the bottom of the tutorials page. The first session (this upcoming Sunday) will look at geometric vectors and establish a strong foundation for being able to solve any type of geometric question you can expect to encounter in this class. As usual, we have a risk-free trial for this tutorial, so come check it out – you have nothing to lose!