# How should I self-study calculus?

So I already took Pre-Calc, and ended up with a B both semesters. I am an incoming senior in high school. My special-ed case manager won't let me take it because she doesn't want to see me panic (crazy, right?). But, for some reason, I really like math. Is there a way for me to self-teach myself Calculus I or Calc I and II before taking it at college? I already have Humongus book of Calculus Problems and PatrickJMT on YouTube (My favorite math youtube channel).

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There is a series, called "The Easy Way." It includes "Algebra the Easy Way," "Trigonometry the Easy Way," and "Calculus the Easy Way." It's been years since I read the books so I don't remember much more about them, though. –  columbus8myhw Aug 25 at 2:44
If you really like math, and you want to take calculus, then take calculus. Don't let people discourage you. –  NotNotLogical Aug 25 at 2:45
A Primer of Infinitesimal Analysis, John L Bell –  mistermarko Aug 25 at 2:58
Being determined to learn calculus is the key to 98 percent of your problems.Be dedicated to your goal.Sacrifice time to master it.At the end, free your mind and smile. –  FreeMind Aug 25 at 3:50
Different schools have different grading systems. If you want to communicate your grade/performance in Pre-Calc, then I suggest you explain what the "B" is. –  BCLC Aug 25 at 6:16

There are many ways you can learn calculus. There are many textbooks out there dedicated to calculus, such as Thomas' Calculus, Stewart Calculus, Spivak Caclulus (more rigorous than the other two and is meant as an introduction to real analysis), high school calculus books, etc.

There is a professor called Paul and he has a lot of good notes on algebra, calculus I, II and III and differential equations on his website. Go on the 'Class Notes' tab and choose the course you want.

If you like video lectures, then I think the best courses are MIT OCW single variable calculus and multivariable calculus courses, which you can find here.

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I second Thomas and Stewart books and MIT OCW. –  BCLC Aug 25 at 6:17
how about apostol's calculus? –  George Dirac Aug 25 at 9:02
Both Spivak and Apostol calculus books are too difficult as an introduction in my opinion. –  user166678 Aug 25 at 12:39

I can't believe no one has mentioned Khan Academy! You can work all the way thru Calculus I and II for sure online. The lectures are great and the assessment format is excellent.

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Download the first edition of Gilbert Strang's Calculus ,available here and get yourself a copy of Adrian Banner's The Calculus Lifesaver: All the Tools You Need to Excel at Calculus, which you can get a used copy of at Amazon for just over 4 bucks. If you carefully work your way through both those sources, you'll be well on your way to mastering basic calculus and the legion of applications that are it's lifeblood. Don't worry about a rigorous formulation right now-your concern right now has to be mastering the basics. 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.

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I second not worrying about rigorous formulation for beginning calculus students. –  BCLC Aug 25 at 7:31

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. Trust me you want a good base to start from in order to get into more theoretical/rigorous calculus.

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 4.0s in both Real and Complex analysis, and I credit a lot of that success to the strong base I built from with that Calculus II course where we used Stewart Calculus books.

Trust me you want to learn to walk before you try to run.

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I second Stewart. I second no Spivak. MIT OCW is okay though I think? –  BCLC Aug 25 at 7:32
I guess I was just being presumptuous in that regard. I will edit my post. Another good resource is Paul's Online Math Notes:tutorial.math.lamar.edu –  Pelto Aug 25 at 15:50
I disagree with the recommendation of a Stewart calculus textbook. They are excessively expensive and lack motivation (in my opinion). One of my favourites for introductory calculus is Morris Kline's Calculus: An Intuitive and Physical Approach. Kline motivates the calculus with intuitive (hence the title) physical problems and does not burden the novice reader with proofs. –  Gahawar Aug 25 at 16:20

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. They offer three calculus courses: AP Calculus AB, AP Calculus BC (link in the sidebar), and plain-old "college" Calculus (I and II combined).

I'm currently taking AP Calculus AB, and I'm loving it (I'm a mathy person). The teacher, Mr. Burger, is beyond fantastic. The way he describes everything makes it as plain as day. It'll cost you \$125 for the AP classes or \$150 for the combined one, but if you're really wanting to learn, I think it's well worth it for the teacher.

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Johns Hopkins Center for Talented Youth uses Thinkwell by the way. –  EverythingTech96 Aug 27 at 0:23

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!

It is customary to teach differential calculus formally and abstractly which completely obfuscates the subject.

Integral calculus is the study of a different property of functions and it too is not about limits.

Bon voyage.

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