### IF YOU registered and have not received a confirmation within 24h, please re-register as your request was not received due to a glitch in the system.

## MATH 263 Final Exam Mastery Sessions

They’re here: the best final review & prep sessions for McGill MATH 263 ODEs for Engineers! **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 develop a solid command of the material and succeed in your class.** To ensure quality and direct support for students, these sessions are capped at ~20 students, so space is very limited; registration is first-come, first-served.

**Full details about the content, costs and discounts on the sessions can be found directly below the registration form.**

**NB: Mastery sessions are**** targeted at students who know & understand the material and want to focus on the finer details of solving problems; very little time will be spent explaining the theory or concepts. Review sessions will include all the same material, but we will spend some time illustrating the concepts and solving questions in full. If you are uncertain as to which session to attend, go with the Review.**

### Discounts:

It’s simple: the more review you get, the better you’ll do, so for every additional session you register for, save $10, $20 & $60, respectively:

- 1 session: $60 for 3h, including notes and practice problems;
- 2 sessions:
~~$120~~$110 for 6h, including notes (for each session); - 3 sessions:
~~$180~~$150 for 9h, including notes (for each session); - 4 sessions:
~~$240~~$170 for 12h, including notes (for each session). - Any (one) session + mock exam, save $10.

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

The following are **tentative** outlines for the individual sessions. Because the groups are small, the content will be catered to the topics you’d most like to focus on.

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

**Sunday April 12th, 12-3pm (M3-37A; $60*): **in this three hour session, we’ll review the techniques for solving first and second order ODEs, focusing on representative exam-level practice problems. Topics will include: integrating factors; separable equations; Bernoulli equations; exact equations; exact equations requiring an integrating factor; the method of undetermined coefficients; the method of variation of parameters; ERF; RRF; GERF & Harmonic Systems (word problems). The focus will be on identifying the correct method & executing it quickly. More information will be provided upon registration. *Discounts available, see above for details.

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

**Tuesday April 14th, 5:45-8:45pm (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 (“advanced methods for 2nd 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 (i.e. shifted Euler) and Frobenius series solutions about regular singular points, using Bessel’s equation as a particular example. Finally, we’ll spend roughly a ⅓ of the session working with Fourier series to illustrate standard tricks to simplify these computations. 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 above for details.

### Mastery 3: Laplace & Systems of Equations

**Saturday April 18th, 11:30am-2:30pm (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; as well as application to higher-order DEs), 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 (distinct, complex and repeated roots / eigenvectors & non-homogenous systems). Additional details will be provide upon registration. *Discounts available, see above for details.

### Mastery 4: Mock Exam

**Sunday April 19th, 12-3pm (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 discussed to help you practice sections that proved most challenging. *Discounts available, see above for details.