Math Calculator App Free Download |LINK|
Marquetta Marteney
Our calculator allows you to check your solutions to calculus exercises. It helps you practice by showing you the full working (step by step integration). All common integration techniques and even special functions are supported.
First, a parser analyzes the mathematical function. It transforms it into a form that is better understandable by a computer, namely a tree (see figure below). In doing this, the Integral Calculator has to respect the order of operations. A specialty in mathematical expressions is that the multiplication sign can be left out sometimes, for example we write "5x" instead of "5*x". The Integral Calculator has to detect these cases and insert the multiplication sign.
When the "Go!" button is clicked, the Integral Calculator sends the mathematical function and the settings (variable of integration and integration bounds) to the server, where it is analyzed again. This time, the function gets transformed into a form that can be understood by the computer algebra system Maxima.
Maxima takes care of actually computing the integral of the mathematical function. Maxima's output is transformed to LaTeX again and is then presented to the user. The antiderivative is computed using the Risch algorithm, which is hard to understand for humans. That's why showing the steps of calculation is very challenging for integrals.
In order to show the steps, the calculator applies the same integration techniques that a human would apply. The program that does this has been developed over several years and is written in Maxima's own programming language. It consists of more than 17000 lines of code. When the integrand matches a known form, it applies fixed rules to solve the integral (e. g. partial fraction decomposition for rational functions, trigonometric substitution for integrands involving the square roots of a quadratic polynomial or integration by parts for products of certain functions). Otherwise, it tries different substitutions and transformations until either the integral is solved, time runs out or there is nothing left to try. The calculator lacks the mathematical intuition that is very useful for finding an antiderivative, but on the other hand it can try a large number of possibilities within a short amount of time. The step by step antiderivatives are often much shorter and more elegant than those found by Maxima.
The "Check answer" feature has to solve the difficult task of determining whether two mathematical expressions are equivalent. Their difference is computed and simplified as far as possible using Maxima. For example, this involves writing trigonometric/hyperbolic functions in their exponential forms. If it can be shown that the difference simplifies to zero, the task is solved. Otherwise, a probabilistic algorithm is applied that evaluates and compares both functions at randomly chosen places. In the case of antiderivatives, the entire procedure is repeated with each function's derivative, since antiderivatives are allowed to differ by a constant.
The interactive function graphs are computed in the browser and displayed within a canvas element (HTML5). For each function to be graphed, the calculator creates a JavaScript function, which is then evaluated in small steps in order to draw the graph. While graphing, singularities (e. g. poles) are detected and treated specially. The gesture control is implemented using Hammer.js.
For those unfamiliar with SMath/mathCAD, it provides easy display of math formulas where you can define variable values and have it auto-populate answers from equations, while commenting inline to explain what you are doing. It lets you work with matrices, easily and perform calculations without the sloppiness of Excel or typing things into a calculator. It is easy to copy and paste formulas between sheets to run the same calculation type for multiple projects.
I think at the risk of emacsifying Obsidian a bit-- it would be awesome to have a simple core calculator plugin, that can be used in a small pane off to the side, actually. Would boost my productivity by a ridiculous amount. And also help people with disabilities not have to switch screens to use a calc app or browser.
Before you downvote this question, I actually want an answer to this. Is the calculator going to give me my derivative? No. Is it going to give me my integral? No. It can sure give me the answer to my integral, but will it give me the calculations? and steps? No.
Something that frustrates me is that I am in post-secondary, and that my level of math right now is not basic. So, like many, I tend to forget the basics of math, like adding fractions, reducing fractions to lowest form fast, subtracting big numbers. Sure, I can do all those, but I would be more likely to make a mistake doing these and loose marks then if I were to just use a calculator.
Teachers want to make sure we "understand" the concept, but I ask, does "understanding the concept" really have to do with our ability to "add, multiply"? Are they testing whether we can do basic arithmetic that we have so long been used to performing with a calculator?
When your working with integration and derivatives, you will get ugly fractions, and adding them, finding denominators, is really a waste of time and effort for me, when the calculator can just do that for me. In the real world I will have a calculator, so why not here? As I said before, what are they testing? Are they testing how I can do basic math, or how I can compute the limit, evaluate the integral, calculate the deriviative?
This is not true, it really depends on the calculator, and there is a whole range of them, from those that cannot even find square roots to programmable calculators with a full CAS. So it would be unfair to give some people an advantage just because they use a "better" calculator. And just restricting certain types of calculators is also very difficult as some might still have some more advanced functions than others. Another solution would be forcing everyone to use the exact same calculator which is also a bad idea.
Instead it is just a lot easier to disallow all forms of calculators. This makes you really strengthen the basic skills (look at it as a positive thing, since you already mentioned that you forgot how to do some of them) and it also makes you think of elegant ways to solve problems instead of memorizing "brute force" attacks.
From what I can see, no MSE user has ever drawn a graph by hand owing to a suggestion of mine. When a reason is given sometimes it is "I'm not allowed a calculator in exams," as though the only possibility for getting a graph is a machine.
I'm sympathetic, because I know plenty of mathematicians who are not particularly good at arithmetic. However, I think that if a test is not intended to test someone's ability at arithmetic in the first place, and is written well in the second place, it should not unduly tax your arithmetic skills. Expressions should "clean up nicely" in the mathematics exam world. When I write an exam, I tend to try to make it so that as little arithmetic computation as possible is required. That being said, some level of arithmetic is needed. That's unavoidable, but probably not to the level of requiring a calculator.
What's more, as amd's comment implies, there is more to mathematics than understanding the concepts, as important as that understanding is. One should learn not just to apply concepts correctly, but to understand when they are being applied incorrectly, whether it was you who made the mistake or someone else. In "real life" (assuming facts not in evidence), I might be asked to look over someone else's work, either as a colleague or as a supervisor. The ability to perform a quick sanity check to see whether it makes sense that the area of a circle $5$ cm in diameter is $79$ cm$^2$, and to identify the likely cause of any error, is invaluable. (You shouldn't need a calculator to figure out what likely happened in this case.)
Exams in other quantitative subjects, like physics or chemistry, may well allow calculators, because the practical aspects of problem-solving are weighted more heavily. I'm not convinced that the same applies to a mathematics course.
This may sound like too strong an opinion, but I see this kind of thing on a daily basis. Often when I see a student in a Calculus class who doesn't have any conceptual knowledge of pretty much any Precalculus topic, and when I talk to such a student to find out more about their background, I would find out that he/she transferred from some other "calculator-reliant" college or school, where they "did everything on a calculator" (this is an actual quote).
When I taught, we permitted students to have a symbolic calculator at all times. The implication for students of this is that the questions in the exam take this fact into account. When such a decision is taken, the questions in an exam become more theoric and/or demand more imagination.
For example, in an exam on optimisation, the focus would be on setting up the right function, not on deriving it or solving $f'(x)=0$. Once the possible optimums were found, the reason for accepting or rejecting them was the important part. The presentation of the solution was also important. We did sometimes have exams not using the calculator, for example on derivating or integrating functions.
One major concern is cheating. People can enter information into their calculators that may give them an unfair advantage on the exam, in essence using the calculator as a "cheat sheet". Having a professor verify that a couple hundred students don't have any information stored in their calculators isn't feasible.
There is also an economic argument: a calculator, especially a graphing calculator, is expensive enough that not all students may be able or willing to buy one. If calculators are useful then they should therefore be banned so that wealthier students don't have an unfair advantage, and if they aren't useful then why allow them?
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