Student Seeking Beginning Calculus Advice

Question

I am a junior in high school and I am seeking advice on where I should begin learning calculus. I have just completed trigonometry as a school class, and I have to admit I enjoyed it. During the course, I consistently felt that learning trigonometry through school was too slow, and it made me want to start learning mathematics on my own. I am fascinated with math, and I want to begin learning higher-level mathematics as soon as possible. As you can probably see, I am a complete beginner when it comes to knowing about the different calculus classes. I do not know the difference between any of the different calculus classes and I am simply seeking guidance as to which one I should begin first.

I would appreciate any advice you can give me.

Thank you for your time.

Note: This question is not limited to calculus advice. I am merely looking for guidance on the next step I should take in my mathematical career. If that means combinatorics, abstract algebra or something else that is unrelated to calculus, I completely welcome that as well. I have just been told that calculus is the most reasonable next step.

Answer 1

Calculus is not necessarily the most reasonable next step. I don't advise self-study in calculus, because there are so many subtleties that aren't obvious to a student.

Find a good book and read it, and do as many of the problems as you can. One of my favorite books for general math, accessible from many levels, is Mathematics: A Human Endeavor by Harold R. Jacobs.

Answer 2

First... I LOVED calculus in high-school, did quite well, especially as it was so very useful in physics, my main subject.

That being said, and after having been a professor of mathematics and physics and statistics, my strong recommendation to students of all interests is to take STATISTICS before calculus. It is so important in daily life and science. Just look at the news today.

Answer 3

It really depends on what kind of background you have etc. But I think a great first place to start learning calculus is Khan academy (I mean as a literal first introduction). This was my first introduction to calculus, and I remember a lot of the ideas being clearly conveyed. Just watch all(/as many as you can) of his videos on derivatives and integrals. I remember spending about 3 weeks/a month on derivatives (basic definitions, power law, sum, product, quotient, chain rule, derivatives of trig functions, exponential, log etc), and spending an equal amount of time on integrals.

Once you get a baseline understanding for what these ideas are supposed to represent, I think reading any calculus textbook will be much more palatable. It doesn't really matter too much what the first book you use is (considering you're only a junior in High school); just pick one which is semi-understandable, and SOLVE AS MANY PROBLEMS AS YOU CAN. By the way, a lot of single-variable calculus is very intimately connected with basic Classical Mechanics. So, if you have an interest in physics as well, I suggest you learn the two topics side by side (kinematics and dynamics using calculus etc).

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Aside from calculus, the subject which I'm finding most useful is linear algebra; it really is the foundation to a lot of more advanced math. As you learn more calculus, you'll realize that the whole idea is to understand a non-linear problem by understanding a simpler, linear problem. So, pretty much by "definition", linear algebra is a must if you want to pursue any further calculus.

Answer 4

Starting with limits and basic single variable calculus provides a strong foundation for thinking more abstractly about functions and the relationships between them. While it can be complex, a site like Khan Academy is a good place to start getting used to the basic concepts in calculus, especially if you're studying on your own. From there, you'll be ready to explore more widely and to discover what other fields catch your interest - the advantage of starting with single variable calculus is that it starts to teach you some of the notation, proof methods, and analytical tools that other fields assume you'll already know.