Here you’ll find information about Math 141 at McGill – if you’re looking for other information about Math 141 sessions with Jacob, try here:
This is one of my favourite courses to teach: it is a first taste of integral calculus and the clever extension of the core concept of calculus (viz. that straight lines can be used to approximate curved lines over relatively short distances), and when presented properly, can be both intuitive and even enjoyable (yes, actually!).
As with many other McGill math classes, the challenge is that the pacing of the class doesn’t reflect the relative importance of topics, and you have little-to-no sense of what is to come later in the semester. As such, although you may not be totally confident about the various methods of integration, you figure you’ll be able to iron out the details later on in the class because, for the first half of the class, it seems like all that will be covered are various methods of integration. Unfortunately, methods of integration are only the starting point, and it’s important to completely master them early on.
After the methods of integration are introduced (by inspection; u-sub; by-parts; trig-integrals; trig-subs and partial fractions), advanced problems will require the combined use of multiple methods. Next, the course will look at applications of the integral to volumes of revolution; calculating bounded areas; arc-length; surface area; continuous, weighted averages and then all of these topics will be seen not only in familiar Cartesian coordinates, but also in a new coordinate system called Polar Coordinates, as well as a new form for describing curves called Parametric Functions. In all of these topics, the ability to integrate any expression is the last step and should be, ideally, taken for granted.
&nd the class doesn’t end there! After blitzing all of the above, you (who, by now, are starting to get a little nervous) are blindsided by the incredibly important topics of Infinite Sequences and Infinite Series, which can appear to have no relation to the earlier material whatsoever and represent a substantial amount of material on their own; material that will form the starting point for Math 222, Math 262 and play an important role in Math 263, Math 314 and Math 315.
Whether or not you plan to join the Mastery Lectures, if you want to succeed in this class, it is critical that you master each topic as it is presented and that you revisit earlier material throughout the term so that when the most challenging material arrives at the end of the class, you can give it your full attention without worrying about ironing out the details of earlier material before the final. In the weekly sessions, I’ll incorporate regular review of earlier material throughout the entire semester and push you to master the material throughout the entire semester so that when the final exam arrives, you’ll feel confident in your ability to succeed.
Beyond the Weekly Mastery Lectures that I offer, I will also run, if there is sufficient interest, WebWork Workshops, Midterm Mastery Prep and Final Exam Mastery Prep to accompany you all along the semester.