Help Self-Studying Calculus

Question

I wanted to learn calculus but I have been told that you can't learn it without first learning elementary algebra. Can someone help me devise a plan for self-study because I don't know were to begin.

Answer 1

From what you have shown, I don't really know where you are. Often times, I hear people making calculus seem like it is something extremely hard. In my opinion calculus isn't something scary if your algebra is strong. I will assume that you already know what a variable is and know how to simplify expressions, graph lines, and graph functions. If you have not mastered these yet, do so. From here it's just learning some tools and mastering concepts that will get you ready for calculus.

Some tools that you will probably need (I listed all I could think of):

-linear equations, slope

-quadratic formula

-line of symmetry for a quadratic

-completing the square

-multiplying linear expressions together

-factoring quadratics

-factoring $a^2-b^2$

-system of equations

-square roots and conjugates

-degree and multiplicity

-rational root theorem

-graphing polynomials (without just plotting points)

-factoring $a^3+b^3$ and $a^3-b^3$

-polynomial multiplication

-polynomial division

-synthetic division

-exponents (especially negative and non-integer)

-Pythagorus theorem

-trig functions

-graphing trig functions (without just plotting points)

-trig identities

-exponentials

-logarithms

-conic sections

-limits

-the definition of a tangent line

I would recommend throughly studying each area individually in this order, until you get a sense of intuition when studying them. You may search on YouTube the topics, or go on Khan Academy if reading books is not your thing. Good luck!

Answer 2

I would advise you learn the fundamentals first. For instance, start with a book like Lang's Basic Mathematics. Once you have thoroughly learned this material, you should follow the traditional pre-Calculus curriculum. Learn about exponential, trigonometric, and other functions- some of this should be included in Lang.

After that, you might consider a book on elementary set theory, such as Paul Halmos' Naive Set Theory, just for some of the introductory topics.

Then you can most likely jump into Calculus. Ian Stewart's books are fairly good and clear if your interest is the applications of Calculus. You could supplement this with Spivak's Calculus. This is just my suggestion.

Answer 3

I have managed to self teach my self up through multi variable calculus by doing the following:

First you are going to want to make sure you have taken both Algebra I and II (at high school curriculum standards), I've found that if you haven't taken these yet, these can be pretty easily grasped through reading books on them.

Next I would recommend taking Pre-Calculus (i.e. Trigonometry), once again I managed to learn these concepts through reading a book and practice problems.

Finally you are ready for calculus; my recommendation for this is that you learn it through online courses that have videos rather than through books, which are harder to comprehend in my experience. I would recommend the following sites for learning calculus:

-Calculus I and II: Coursera (I took the courses offered by Ohio University)

-Calculus III and Above: MIT Open Course Ware (These are less of online courses but rather video lectures and lecture notes; this has been the best site in my opinion for higher level courses)

Answer 4

Israel Gelfand's books (Algebra, Trigonometry, Functions and Graphs, etc.) and Harold R. Jacobs' books (Mathematics: A Human Endeavor, Basic Algebra, Geometry) are a good place to learn the mathematics that comes before calculus.

After (or during) these, you can get a good sense of the calculus with Silvanus P. Thompson's book Calculus Made Easy. Also Paul Lockhart's Measurement can be read at any stage of this process to get an intuitive sense of the calculus and its relation to geometry.

Then, as Antonios said, you should learn some set theory and/or logic. I don't recommend Halmos as a book to start off with, but there are plenty of books if you look. If you want to study calculus with the tools of set theory, I suggest Spivak's Calculus.

Also it's a good idea to learn some physics along the side, because when calculus was developed in the 17th Century, mathematics and physics were basically the same thing. For this I suggest Sears and Zemansky's University Physics (be sure to get an early edition, like the 5th, because the later ones suck. You can buy an early edition cheaply from AbeBooks) and the Feynman Lectures.