<p>Hi all
I'm currently a senior who has committed to the University of Toronto this upcoming fall. I will be studying engineering, so I obviously have to be proficient in math. I was accepted to their engineering program even though I have never taken Calculus. They allow students without Calculus to present the Math 2 SAT2.</p>
<p>Although I did score a 780 in the Math 2, I left out most of the questions that I now have learned in pre-calc (took the test in november). I really don't know how doing well on Math 2 is a substitute for AP Calc, so I am slightly worried about my upcoming freshman year. </p>
<p>If I wanted to brush up on past topics and get a head start on some of the Calculus concepts, how could I do this over the summer? I will be in different countries in July and August, so I don't think signing up for a summer course is a viable option. If I were to buy and study a book, which would you guys recommend?</p>
<p>Also, what are the big topics learned in Calculus 1? Just so I know what to study.</p>
<p>Thanks :D</p>
<p>MIT has the course online for free</p>
<p>[Free</a> Online Course Materials | Audio/Video Courses | MIT OpenCourseWare](<a href=“Search | MIT OpenCourseWare | Free Online Course Materials”>Search | MIT OpenCourseWare | Free Online Course Materials)</p>
<p>Wow, thanks!</p>
<p>Would single variable calculus be the equivalent of Calc 1? Or is multi variable calculus part of it too?</p>
<p>Single variable is generally calc 1 and 2, multivariable is calc 3. Calc 1 (at least for me) went up to general integration, calc 2 is where the techniques of integration started.</p>
<p>All of the above postings are good sites for getting a leg up on Calculus. Most engineering programs are structured “assuming” that the student is starting with Calculus I in the fall term of their freshman year.</p>
<p>It’s not a bad idea to do the same thing NEXT summer to get a leg up on either Multivariable Calculus (also called Calculus III) or Linear Algebra…whichever you choose to be the 3rd course.</p>
<p>Thanks for all the links guys! Just watched the MIT lecture on Linear Algebra. Very interesting, although he only went over basic concepts.
University of Toronto actually has linear algebra and calculus 1 scheduled in first semester for all engineering students. </p>
<p>I’m assuming that Calculus 1 deals mainly with Limits, Derivatives, and Integrals. Anything else I’m missing?</p>
<p>If you are perfectly comfortable with pre-calc and trig (if not, then self-study those first) then just get any book on teaching yourself calculus (specifically one meant for the self-studier, not a textbook), and go through it, doing all of the problems and correcting yourself when you get one wrong. Did I mention to do all of the problems?</p>
<p>You’ll start with learning about limits, then the derivative (differential calc), after mastering that you’ll start with integrals (the reverse of the differentiation process). Integral calc is where people start screwing up and it’s all because they lack the algebra skills. So you need good algebra skills, ESPECIALLY WITH TRIG. Trig will come up, well, pretty much everywhere, all of the time. You’ll learn that it’s not some branch of math that just pops up when you need to deal with triangles, you’ll be using the cos, sin, and tan functions for the rest of your life.</p>
<p>Anyway, just do lots of problems and do them over again if you get the wrong answer.</p>
<p>And never use a calculator or math program to do anything for you that you can’t already do yourself.</p>
<p>Ah alright. By studying up on trig, what exactly should I be focusing on? It was quite a while ago, so I’m not exactly what the topics are called. Thanks :)</p>
<p>Trig: Identities, properties, unit circle, and how to figure out everything you can with that.</p>
<p>People are scared of trig functions in a lot of my classes, but they really aren’t all that bad if you put some time into them and just keep it up.</p>
<p>The biggest thing is knowing the different relationships between the trig functions and their inverses, reciprocals, etc. Knowing the values of the trig functions at key places is very helpful as well.</p>
<p>I just finished calc II this spring, and my rather weak knowledge of trig plagued me constantly all semester.</p>
<p>The MIT course is a bit advanced for a beginner. I would first buy an AP Calculus Review book (Barrons is the best IMO). I would use that along with Pauls notes ([Pauls</a> Online Notes : Calculus I](<a href=“http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx]Pauls”>http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx)). You can use the MIT review at the end, but you really won’t grasp everything in the videos without a decent background.</p>
<p>As an engineering student you’re really going to need a strong math basis. I would suggest you give yourself a quick introduction into linear algebra over summer. Once again Pauls notes along with Introduction to linear algebra (Gilbert Strang) will help you with that.</p>
<p>Your math SAT score really won’t help you walk in on your college courses. You’ll probably grasp the topics quickly, but it is worth your time to self study over summer.</p>
<p>Best of luck!!!</p>
<p>I’d go with Khan Academy. It might have a “lowest common denominator” teaching method, but it’s pretty nice regardless. Really nice and useful way to learn the material because it was made to be used to learn independently.
MIT OCW is nice, but at the same time it often feels like you’re just using a good resource in a not-so-productive way since it was given as a class lecture for students who actually have books and coursework.</p>
<p>I think Khan Academy for basics and Patrick JMT and MIT for a higher understanding is the way to go. Khan is very good at getting across the basic points. Once you got that down you can actually understand what the MIT professors are saying lol.</p>
<p>I would disagree that the MIT course is too advanced for beginners. It is meant for Freshmen. Just pay attention as if it was a real class (If you think about it, it really is)… That’s how I learned calculus and I really would not recommend review books. Review books give you an abridged version of the text, which will make you inclined to just memorizing formulas. The lectures give the intuition behind and if you actually take time to dissect the lectures, you will learn so much more than the formulas…</p>
<p>I don’t think his goal is to become proficient in calculus. I believe he wants to have the calculus skills to succeed. </p>
<p>I’ve watched a few of those lectures and there are far too many proofs for an introductory calculus course. Yes those of us with a calculus background may understand, but for a high school student coming out of pre-calculus…</p>
<p>Just an anecdote: that’s how I learned during the Summer of my Junior year coming out of pre-calculus. I took notes as if it was class and looked over them over.</p>
<p>I would do a google search for a calculus syllabus from whatever college you’re going to, or any generic one from any college, buy a text book and start going through the sections on the syllabus. maybe buy one of those For Dummies books or study guides from a book store. use sites like khanacademy . org for reference, study the chapters and bang out tons of the problems in the back of the chapters. try to gain intuition of whats going on, not just the mechanics of the problems. I’ve taken most of my maths as online classes, the only difference between them and what you want to do is that they put you on a schedule and make sure you learn the material with exams and homework, theres no reason why you wouldn’t be able to learn this stuff on your own with a bit a discipline. I’m not sure if you’ve taken the precals yet, but you’ll want to make sure you become proficient in those, along with trig, before you really start in calc. If you havent taken them, reread my post and replace “calculus” with “precalculus”.</p>
<p>Thanks for all the responses. I’ll probably do a combination of all these to help me develop an understanding of Calculus. I will be taking Calculus 1 first semester, so I’m just doing all of this so that I won’t fall behind. </p>
<p>What would be a good book that contains problem sets that I can practice? Math seems like a subject where practice really helps, so which book would allow me to do this? A textbook? OR will a review book have a large enough range of questions that will allow me to practice? </p>
<p>Also, is there any way I can use high school resources to help as well? What could I ask my teachers to help me with?</p>