Calculus is a massive & scary set of new ideas for most students.
Here's what you need to know when starting to learn Calculus.
This might not be the answer you were looking for, but the reality is: It depends.
Calculus itself is actually quite easy to learn.
The reason most people tend to struggle with it is not Calculus itself. It's because they didn't understand Trigonometry and Algebra beforehand.
A good way to think of Calculus is to think of it as a continuation of Algebra classes. “Advanced Algebra,” if you will.
If you don't understand Trigonometry and Algebra when starting to learn Calculus, you'll likely struggle with Calculus and find it hard to learn.
However, if you have a solid foundation in Algebra and Trigonometry, you should do well in Calculus and understand the basic concepts quickly.
Once you get the hang of it, you might even find it easier than Algebra, as problems usually take a lot less time to solve.
Your learning experience will obviously also depend on your teacher and your textbook. I have put together a list of the best calculus textbooks here.
This depends on the “amount” of Calculus you want to learn.
If you only want to understand the basic concepts of Calculus, it won't take you much longer than a few hours.
Learning “high-school” Calculus takes roughly 120 hours of class and an additional 90 hours of self-study.
Learning the same in College would take about 60 hours of class and 80 hours of self-study. Classes in College are typically faster-paced, hence the time difference.
Learning “college” Calculus would mean adding roughly another 90 hours of class and another 150 hours of self-study to “high-school” Calculus. This would bring the time spent to roughly 380 hours.
To extend the “college” Calculus to include undergraduate & graduate analysis, add another 150 hours of class and 270 hours of self-study to “college” Calculus.
Obviously, these numbers aren't factual and are only rough estimates, but they should give you a good idea of how long it will take to learn Calculus.
Before I give you advice on how to learn Calculus the easy way, I want to stress this again:
Please make sure you have developed a good understanding of Algebra and Trigonometry before you even think of learning Calculus. Calculus is “advanced Algebra,” if you will, so there's no point in trying to learn Calculus if you don't understand the basics of Algebra.
My second piece of advice would be to learn Calculus in a structured way.
Below I have lined out the major topics of Calculus in the order that makes the most sense to me.
Thirdly, and I can't stress this point enough, solve problems.
If you plan to develop a good understanding of Calculus by listening to lectures or reading books, I will have to disappoint you.
Calculus is way too complicated to understand just by listening and reading.
The only way to get a good idea of Calculus is to practice solving problems.
Lots of problems.
The more problems you solve, the better you'll get at it.
The easiest way to learn Calculus would therefore be to first revisit the major topics of Algebra again and make sure you fully understand them.
Then start with the first topic of Calculus (Rate of Change) and before you move on to the next one solve problems. Only once you understood the topic AND solved some problems move on to the next topic.
Yes, you can learn Calculus online.
However, please keep in mind that learning Calculus Online will take good time-management skills. It's a lot easier to procrastinate when you learn online compared to when you learn in a classroom.
One advantage to learn Calculus online is that you can use technology to help you understand better.
You can use a graphing calculator for example to understand how an equation's graph looks like.
There are two options when learning Calculus online, paid and free resources.
Below I put a list of the best free resources to learn Calculus.
Paid resources often offer more structure and therefore speed up your learning process.
A great place to find paid programs for relatively cheap is Udemy.
But you have to keep in mind that this will require a lot of self-discipline and motivation.
You'll have to come up with a schedule and stick to it.
The schedule should ideally also include your sources. If you'd write down “Understanding the Rate of Change,” you'll likely fail. The reason for that is that there's just too much information available.
You'll start on one website or video, then jump to another to research a term, and before you know it, you've opened 10 different websites and have no idea where you started.
This will demotivate you very quickly, and with no one being by your side, you'll likely get distracted quickly.
Instead, I would urge you to research beforehand and write sources (e.g., Khan Academy – Rate of Change) next to your schedule.
If you do this, you'll have a clear plan in mind, and it'll be easier to stick to your schedule.
If you learn Calculus on your own, it will take you roughly half as long as learning it in a “high-school” class, so about 150 hours of self-study.
This number will obviously change depending on how serious you're about learning Calculus. If you take lots of breaks and get distracted easily, it will take you much longer to understand Calculus.
You can think of Calculus as “Advanced Algebra,” so you should definitely learn Algebra first.
Before starting to learn Calculus, you should develop a good understanding of Algebra and Trigonometry.
Almost everything about Calculus comes down to applying a concept of infinity to Algebra.
When you first start to learn Calculus, you will probably think it's much more complicated than Algebra.
However, once you develop a good understanding of the basic concepts of Calculus, you'll likely find it easier than Algebra.
The reason for that is that Calculus problems usually take way less time to solve than Algebra problems.
I also found that once I understood Calculus, Algebra made much more sense to me.
Calculus provides answers to many unanswered questions from Algebra.
For most students, Calculus is one of the hardest parts of mathematics.
It doesn't have to be hard though! As explained above most students don't struggle with Calculus itself but with Algebra. Before you start learning Algebra make sure you understand all the major topics of Algebra and then start solving problems, that's the best way to learn!