# Requirements to learn calculus

I always was non math background student and programming is my hobby. I was attempting to program code instruction given here. Since I don't know calculus I'm stuck. I would like to know what are the things I need to learn before I start learning calculus? I can solve some basic algebra problems. Could anyone please guide me? Thanks.

• You need a glossary, and perhaps a book on numerical methods. Feb 1 '17 at 0:44
• Maximum = peak. Minimum = bottom. First derivative = dy/dx = slope. Second derivative = d²y/dx² = rate of change of the slope. (In other words, find the slope near one point, find the slope near another point, subtract the two slopes to find a numerator, and subtract the two x values (of the points) to find a denominator.) You can estimate all of these things using a data set and your basic algebra skills. Feb 1 '17 at 0:47
• The slope at a peak is zero (or undefined). The slope at a bottom is also zero (or undefined). The slope just after a peak might be very negative. Feb 1 '17 at 1:05

When I teach people calculus, the big reasons they don't succeed tend to be problems with arithmetic and very basic algebra. For example, students won't know how to compute 2/(3/4), or they'll try to simplify $1/(x+y)$ to $1/x+1/y$. If you can handle this kind of stuff, then you're better prepared to learn calculus than most of my students.

There is some material often taught in a trig or precalculus course that may also be useful, but it's not critical. For example, it may be helpful to know what a function is; to know how to manipulate exponentials, e.g., $e^{a+b}=e^ae^b$; and to know trigonometry. If you don't know about trigonometric functions and exponential functions, then you won't be prepared to do calculus on them.

• Indeed, most of the marks I take out off of an exam are precalc stuff... Feb 3 '17 at 2:24
• @Ben Crowell Thanks for the basics. I could calculate basic arithmetic and algebra. So, I think I need to learn the trigonometry then. Feb 16 '17 at 20:39

Traditional calculus study also requires trigonometry.

Nowadays you will also find some "watered down" calculus texts with no trig functions, intended ironically* for business students.

*You would think business students would be interested in cyclical phenomena, wouldn't you?

• Business students are only interested in the exponential function. Dec 18 '17 at 18:24
• @StevenGubkin Add some complex numbers and those become the same thing Jul 13 '20 at 12:07

From Velleman's Calculus: A Rigorous First Course:

As to the content of the first chapter, it includes (but is not limited to) the following:

• decimal notation, integers, rational numbers, irrational numbers

• sets, subsets, elements, unions, intersections, intervals

• expressions, equations, inequalities

• triangle inequality, Pythagorean Theorem (and distance formula)

• functions, domain, independent and dependent variables, composition of functions

• absolute value function, square root function, linear functions (slope-intercept and point-slope forms), quadratic functions, polynomials, rational functions, trigonometric functions (along with how to use radians, the unit circle, etc)

• @Thanks Benjamin I will look into it. Feb 16 '17 at 20:40

Naturally, it's what they call Precalculus

.. where "they" is whoever's calculus materials you'll be using. While there is some variety, I expect it to include algebra to a few steps beyond the most basic problems, some geometry, and at least the basics of trigonometry. Some curricula also introduce limits in precalculus.

In algebra, you should be comfortable using basic identities including those in @BenCrowell's answer, solving quadratic equations, arithmetic on polynomials, raising polynomials to small exponents, dividing and factoring polynomials, and so on.

In geometry you should understand cartesian coordinates, be familiar with graphing functions, and know the equations for basic shapes. It may be helpful to get the gist of parametric equations.

In trigonometry you should be comfortable solving algebra and geometry problems involving trig functions or which require trig functions for their solutions, and using the common trig identities to rewrite expressions. It may be helpful to know something about the relationship with complex exponents and/or about hyperbolic functions.

But that's for learning Calculus overall, and I've been somewhat inclusive to hedge against variety in calculus curriculum. If you're studying on your own you can probably backfill as needed to a large degree. If you're only interested in this one problem and have access to knowledgable people (or can hire a tutor) you can probably focus pretty narrowly and learn a small subset just sufficient for this one problem. Glancing at the problem, it touches on techniques from numerical analysis and statistics, so at some point it might be better to consult a knowledgeable person and target specifics rather than to try to (in effect) take all of the courses involved. (That might come close to getting a math minor - which I wouldn't discourage, but it depends on your goals.)

The answer depends on the level you want to learn calculus at. I'll assume you want to learn it the way most North American students do, with little emphasis on proofs and theory.

In that case, the content of Serge Lang's Basic Mathematics is more than enough preparation.

Alternatively, Marsden and Weinstein's Calculus I has a self-test section at the beginning to tell you if you can start learning calculus directly, if reading their review chapters is enough (and which ones), or if you should go back and learn from a precalculus book.

You should consider (and the answerers) how much you really need/want to learn. Perhaps only some basics, perhaps only a specific problem or two are really what you need for the task(s) you have in front of you. If you want to learn calculus as a real topic than that will be a bit more work and you should make sure you want that enough. Even so, given what you tell us, I strongly urge you to work with "easier" books than hard ones. You will get more out of something you don't give up on. (Can always go back and do it harder if that is a need, later.)

1. Take a look at "Calculus Made Easy" or "Calculus for the Practical Man". Both are written in a nonpompous style and are relatively easy in excluding some harder topics. They are available as free (legit) pdfs; Google search for best download. After you get one of those (I quite like the Thompson one in being almost fun to read), take a look at some of the book, see if you can learn from it, and consider how it pertains to your programming tasks.

2. The suggestions about Precaculus and being up on algebra (you sounded weak) were very good ones. Not only is it hard to work on calculus with weak algebra but these are topics that are useful themselves (and perhaps even more applications than calculus; for example exponentials and rational functions are common in oil EUR programming on Tableau, Spotfire and Excel)

A cheap, good text in this area is Frank Ayres Schaum's Outline First Year College Mathematics which covers everything up to Calculus other than Geometry (which you don't need for Calculus) and even has a little intro to Calculus (which might be all you need or at least help you before you make the jump to a calculus text.)

Here is a link but you can try other booksellers. I recommend the original 1958 version (lots of used versions available on the net).

https://www.amazon.com/Theory-problems-first-college-mathematics/dp/B0007DPVM2/ref=sr_1_1?s=books&ie=UTF8&qid=1513575322&sr=1-1&keywords=Schaum%27s+Outline+of+first+year+College+Mathematics

1. If you have worked through the Ayres, you could look at "normal textbooks" like Thomas Finney, Swokowski, Stewart, etc. But I worry that they are a little too formal (they get sold to professors or committees that select them and are used when a teacher is available to support with lots of lectures). Better off with one of the suggestions from point 1 or perhaps some Dummies brand book or another Schaum's Outline just on calculus.

2. Disagree with the Velleman text. It's not as bad as it sounds, are some good aspects to it. But it's not a good suggestion for someone who self identifies as non mathy, mature, and needing calculus for work. Would suggest it instead for a precocious math student self studying or even for a regular (strong) class. There are also some places where it really emphasizes precision on limits and introduces new notation even. Just not the right thing to worry about with someone who didn't make it to calc when he could have in school.

3. Also look at Khan academy.

There are both video and problem assistance and the training is pretty supportive and clear and gentle. It may also appeal to you since you are into programming and it is a little techie in terms of the interfaces (some video game aspects of the problem solving, how the lectures are done on YT with an etchasketch). Even just watching a quick video here might help you get a little motivated or intrigued to learn more.

The Calculus is all about limit concepts. So, you need to understand some basic computations with all type of functions like polynomials, exponentials, logarithmic, trigonometric, inverse trigonometric, hyperbolic function... and more.

In order to visualize the Calculus concepts, you need to know the geometric shapes in 2D and 3d and its properties.

If you want to optimize something, you have model/function and you need to find the critical points of the function/model. so, to find those critical points or something. You need to solve the equations, sometimes systems. So, you would know Algebra.

so, to start learning Calculus. My suggestion is you would get through Algebra ( Basic, Intermediate), Geometry( 2D and 3D) and Trigonometry.

Also, you must familiar with all types of coordinate systems, rectangular, polar, cylindrical and sphere.

if you know all the concepts well, before start learning Calculus. Then, you enjoy the Calculus. It is great fun.

I wish you all the best, happy learning. :) Thank you.. ~Satya from India.

Explain exactly why you need to learn calculus in order to program an algorithm. If you can identify a specific need, then you can focus on that specific requirement or need.

Calculus usually consists of 3 general topics - differential calc, integration and vector calc?

Which one of these do you require for solving your programming problem?

Regards

Before starting calculus you must know the following topics.

1. Relations and functions.
2. Trigonometric functions.
3. Combinatorics.
4. Sequences and series.
5. Infinite series (exponential series, geometric series, logarithmic series, and binomial theorem for any index).
• In the educational system where I live (the US), 3, 4, and 5 are not assumed as prerequisites for a calculus course. Actually, 4 and 5 and part of the curriculum for 2nd-semester calculus.
– user507
Jun 9 '20 at 13:55
• I disagree with most of your list. (1) I agree that you need to understand functions reasonably well before getting into calculus, but more esoteric relations don't generally come up. (2) Trigonometric functions are entirely unnecessary as a prerequisite. They often come up as examples, and a lot of books really like to harp on trigonometric substitution, but this is orthogonal to actually learning or understanding calculus. Jun 9 '20 at 20:16
• (3) I can only think of two places off the top of my head where combinatorics comes up: combinatorial identities are often used in proving the binomial theorem (though there are other approaches), and can come up when discussing infinite series. In both contexts, previous familiarity with combinatorics is not needed. (4) Sequences and series are usually a topic in calculus classes (in the US, anyway). There is absolutely no need to be familiar with them ahead of time. Jun 9 '20 at 20:19
• (5) Similarly, it doesn't make sense to talk about infinite series until you know what a limit is. Once you have defined a limit, you are doing calculus. Infinite series are definitely part of a calculus class, and not a prerequisite (my objection to point (4) notwithstanding). Jun 9 '20 at 20:19