And you will encounter questions in calculus that first need to be transformed prior to solving and you will need to remember your techniques for isolating the variable. Because you will be expected to analyze functions to determine maximum and minimum values as well as finding the domain and range. While you can definitely do this algebraically, if you can remember what the graph looks like, you will have a leg up on your classmates.
Because these skills springboard you to the answer your seek without getting bogged down with tedious algebraic steps. Just knowing how to find vertical and horizontal asymptotes will make you a superstar. The properties for exponential and logarithmic functions are so intimately connected to the properties for derivatives and integrals, that you will smile every time you use them.
Furthermore, just knowing how to simplify these transcendental functions will save you time when having to take higher order derivatives or when simplifying integrands. Yep, you read that correctly, the fancy word transcendental simply means exponential, logarithmic and inverse trig functions…. In particular, you will need to remember your Unit Circle and radian measures as well as the basic trig identities. All throughout calculus, you will be substituting radian measures into various equations or expressions in order to evaluate limits, derivatives, and integrals; therefore, solid trig skills are a must!
In fact, just knowing knowing your Unit Circle and remembering your Pythagorean Identities can move you to the head of the class. While this test does not cover every possible problem or topic that you will encounter in calculus, it gives you a very good idea of what you are expected to know and also helps you to identify any gaps in your understanding, if there is any. Having a good understanding of Trigonometry is essential if you want to succeed in Calculus.
You will need to be comfortable with using the Unit Circle to solve problems with Trigonometric functions. We also suggest reviewing algebra and geometry as they are both fundamental concepts of calculus. If the textbook is available to you, start reading chapters and familiarizing yourself with new and old topics. Textbooks often have a review section of prior material before introducing any new concepts. Take advantage of this to ensure you have a strong base understanding of previous math topics.
If you feel unsure or confused, ask a tutor or a friend for help. Another concept covered in Grade 12 Calculus is logarithmic functions. Here, students will revisit logarithmic functions concepts seen in Advanced Functions but in greater detail. Calculus introduces the natural logarithmic function:. Students will need to make connections between these functions as one equation can reverse another. The relationship between the logarithmic function and the inverse of the exponential function is evident when drawing graphs as they reflect each other.
Limits and Derivatives are two new concepts introduced later in the course. If you have the opportunity to learn about these new topics before you get started, we highly recommend doing so. These concepts have new notations and definitions that require lots of time to learn and understand. The limit of a function explains the behaviour of the function near a specific point. A derivative is used to determine the instantaneous rate of change of a function with respect to the variable.
For example, it may be helpful to know what a function is; to know how to manipulate exponentials, e. If you don't know about trigonometric functions and exponential functions, then you won't be prepared to do calculus on them. 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.
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. 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. 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. 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 version lots of used versions available on the net. 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. 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.
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