Is it possible to learn calculus by yourself

I started the class on Monday and wrote the exam on Friday afternoon. This meant I had roughly 4. First though, why bother learning calculus at all? Beyond being a required course for my challenge, I think calculus has an unfair reputation as being either too hard or not useful enough to bother learning.

Calculus is a tool that allows you to solve really interesting problems, that are much harder to solve without any knowledge of calculus. For learning computer science, for example, calculus allows you to run machine learning algorithms in artificial intelligence, render 3D computer graphics and create physics engines for video games. More, learning calculus in this challenge is also a statement about the benefits of theoretical versus practical knowledge.

A lot of people have been criticizing my challenge for not doing enough programming. However, part of the criticism, is weighed against learning theory in general.

A common misconception is that the best way to learn is simply to just go out in the real world and do things, and only learn theory when you absolutely need it. But this misses the purpose of learning the theory behind ideas. Learning theory broadens the types of problems you can imagine possible solutions to.

Learning the theory behind algorithms, machine learning, graphics, compilers and circuitry gives you the ability to think about and take on more interesting problems. Math is about solving problems quickly. If you think that being fast is a sign of being good at math, you are setting yourself up for failure. Researchers at the University of Chicago have demonstrated that anxiety even affects students who excel in math.

Knowing how to solve a problem is important, but knowing why that solution works is more important. If you learn only the rules and procedures without learning why they work, what will you do if you forget it?

Who knows? Before you get started, you should brush up on these essential skills: Algebra. Be able to solve polynomial, linear, and quadratic equations.

Understand the properties of exponents. Know the properties of logarithms. Understand what a function is and how to represent it on a graph.

Know how to manipulate functions and be familiar with terms related to functions, like domain, intercepts, and range. Be able to compute the area of shapes and volume of shapes. Be able to reason about a coordinate plane and equations for parallel and perpendicular lines. Know what sin x , cos x , and tan x functions represent and how they are represented on a graph.

Pick Your Sources For learning Calculus, you have three options for sources—books, free online resources, or self-paced courses that you need to pay for.

Here are some to check out: Khan Academy. This popular site features courses in everything from Art History to Physics. This link will take you to the Calculus page. Many of the courses on the website start with middle school concepts and work up, so this could be a useful resource if you need to review a prerequisite subject.

MIT OpenCourseware. MIT was one of the first universities to upload courses with lecture videos. Some courses include homework assignments, notes, and tests. This is a hodge-podge site with everything from problems, animations, online textbooks, tutorials, and videos.

An excellent resource for additional problems, explanations, and tools. Calculus for Beginners and Artists. A straight-forward approach. It is a text-only resource, but the writing is clear, and the course is well-organized. If you want to use YouTube, this resource would be an excellent way to ensure you are logically hitting the concepts.

Come Up With a Schedule Without a schedule, chances are good that other things will keep coming up. Partner Up Maybe you already have a support group or circle of friends who will keep you on your toes and share your successes. Plan to Reward Yourself Decide how and when to reward yourself.

If you study both those sources diligently, you'll be well on your way to doing so. You can worry about a careful formulation after that. One step at a time. Stewart Calculus. Don't do Spivak, that is just too much in my opinion. Just start from the beginning of any edition of Stewart Calculus.

Section by section work a good amount of problems, to ensure you are learning. This is coming from someone who took calculus in highschool, then went 3 years in undergrad before realizing their passion was in math. Took calculus II at my university and didn't even know the unit circle. One year later I found myself in noneuclidean geometry, probablity, real analysis I and topology in the same semester.

Got 4. Depends how you naturally prefer to learn, but if you're like me and like an intuitive taste before the formalities, Calculus I and Calculus II are very good video introductions on Coursera.

There are many additional courses such as Massively Multivariable Open Online Calculus Course with gradual "inline" mini assessments. Also, I find the University of Colorado's video lectures absolutely indispensable. I would recommend Thinkwell Homeschool. You don't have to be a homeschooler to use it though I am. It can be taken as a full course or used to supplement another. The teacher, Mr. Burger, is beyond fantastic. The way he describes everything makes it as plain as day.

I took differential calculus twice at two different colleges and it still took me at least another decade before I understood it. It is a simple subject but not the way it is taught. Differential calculus is the study of one particular property of functions. So it is absolutely necessary that you clearly understand what functions are including graphical form, what it means that they have properties including point properties, and what some of their properties are before you go on to differential calculus.

The point property being studied in differential calculus is the slope aka "rise" or "grade" of a function which is expressed as a different function of the same independent variable as the original. Differential calculus is not about limits. The use of a limit is simply a device to enable us to formally obtain the derivative of a particular function.

In practice only mathematicians use it. As an analogy, a gun is used by a holdup man but holdups are not about guns. In fact the slopes of a constant function and a linear function are clear without using a limit.

You'll learn the derivatives of the elementary functions, notation for the derivative, properties of the derivative, applications of derivatives, higher order derivatives, and why some functions don't have a derivative at some points or even at any point!