# Self-teaching Calculus?

by Aes0p
Tags: calculus, selfteaching
 P: 2 I hope this is the correct forum for this thread. I know there are many threads on this but my situation is a little more specific. I'll be a freshman in college this fall and will be taking Calc 1. In HS I took Alg 1,2,3 (useless class, same as alg 2... I had a scheduling conflict), pre-calc. I made A's in all those classes pretty easily but I wouldn't say I'm good at math. I guess I'm average. Anyways, I want to try to teach myself some calculus before I enter college in a couple months. I would like to really learn the subject so I would rather cover less material but learn it as well as possible. I'm basically looking for the best resources (online, preferably) to use to teach myself. I'll try to stop rambling and get to the point... How should I begin this process? What are some good websites/video lectures to use? I'm a little lost with what to do. If it helps, I have a calculus book by Stewart (Concepts & Contexts, 2nd ed.) and also an Analytical Geometry and Calculus book from the late 50s. I appreciate any suggestions!
 P: 186 I suggest that you stay away from multivariable calculus. Any arguments in support of taking m.v. calc could be used to justify teaching yourself all sorts of advanced courses, which is not advised. I would study the following topics/ideas, whether in YouTube videos, books, wb resources, etc: 1) techniques for evaluating limits when direct substitution fails (avoid the delta-epsilon limit) 2) difference quotient/definition of the derivative 3) basic derivatives. These are on the inside cover of most calc books. 4) the CALCULUS definition of the (natural) logarithm. 5) fundamental theorem of calculus (of course!) calculus is really not that bad. It gets a bad rep because it's heavy on algebra and courses usually move at a steady pace. Good luck!
P: 15

## Self-teaching Calculus?

Well, I took Calc I, II, and III my freshman year of college so I know what material you want to know for sure.
1. Basic derivatives (1st order, 2nd order, etc..)
2. Series (Taylor and Maclaurin)
3. Limits (need this before you do series)
4. Convergence/divergence
5. Trig identities
6. logarithms
7. trig substitutions
8. quotient/product rule

There are other topics but these are the most CRUCIAL. If you understand these, you'll do just fine. Like "The Chaz" said, Calc isn't really that bad. Have fun!!!
 P: 2 Would watching the MIT videos be sufficient or will they be more difficult to follow since it's MIT? Also, has anyone read Calculus Made Easy (1914) by Silvanus P. Thompson? I'm probably over thinking this....
 P: 175 Sylvanus Thompson is a bit dated but fun and easy to read. It is more a book for Arts majors. Not very rigorous but good for many students. You can find Gilbert Strang's book at books.google.com. He teaches at MIT and its a first class book. Several others you will encounter with a google search. Integration is just multiplication with one of the elements changing. And since multiplication is just repeated addition [ 4 x 3 = 4+4+4 ], it comes down to addition. Area under the function from one x value to another x value. Differentiation is just division and since division is repeated subtraction, it comes down to subtraction. Instantaneous slope of the tangent line at a point on the function.
P: 18
 Quote by The Chaz 4) the CALCULUS definition of the (natural) logarithm.
What would that definition be? something other than the inverse of e^x?
Mentor
P: 19,758
 Quote by maxbashi What would that definition be? something other than the inverse of e^x?
$$ln(x) = \int_1^x \frac{dt}{t}$$
 P: 273 I think that the Stewart text should be enough for you. You could maybe find a tutor/mentor who can maybe provide you with guidance or create "deadlines" for things to keep you motivated. What others have listed is basically whats inside the Stewart text. And even if you don't FULLY understand what you're reading just the fact that you'll be familiar with it all once you take the course provides you with a head start. Calculus isn't hard. It may seem like it is at first, but if you just sleep on things it always helps and once you're done you'll look back and think that was easy! Good luck!
 P: 529 My honest advice is to stay well away from the M.I.T. videos. At first I thought they were really hard and was kind of scared away from them. I went off and learned all of this stuff seperate from these videos & I would go back and watch videos on topics I now understand (having previously failed to get it) and no, it's just the videos that are at fault. Terrible! I then tried an experiment, I watched ahead with those M.I.T. videos to see would I learn anything about, say, improper integrals etc... but no, the videos take about 5 seconds on the important thing (which is not given the importance it deserves) and then you go off on a tangent... Stick with the books you have. If you get stuck at any point, www.khanacademy.org , www.justmathtutoring.com , http://www.uccs.edu/~math/vidarchive.html , are all video lectures based on the calculus course. The uccs ones are based off the Stewart textbook and are helpful but the other two are shorter and better, see what you think! Basically, get your algebra, trigonometry and logarithms working perfectly and calculus will be extremely easy. The important idea's in the course will be multiplying by 1, i.e. $$\frac{\frac{1}{x}}{\frac{1}{x}}$$ is actually just equal to 1 but will be used for limits! Never dividing by zero! i.e. if you're dividing by zero you're either doing the math wrong or are encountering a limit/derivative/l'hopital etc... Important to keep an eye on this as you might take a derivative but need to see where your original equation divides by zero - that can trip you up! the pythagorean theorem doing algebraic tricks! some trigonometric substitutions using the area formula's for triangles, squares, etc... These are the things you'll be using as you learn all of the topics the guys/girls listed above in ths thread, enjoy!
 Quote by sponsoredwalk The important idea's in the course will be multiplying by 1, i.e. $$\frac{\frac{1}{x}}{\frac{1}{x}}$$ is actually just equal to 1 but will be used for limits!