Quick Math Generator

[Candi Ruman]

Wehad snow and rain today and the wind is coming up. That is the kind of conditions that usually cause a power failure around here. I've had my pull cord electrical generator for 5 or 6 years now and I only use it when the power fails. The problem is getting the generator to start when the need comes up. More often than not I spend 10's of mins pulling on the cord and adjusting the choke to get the thing started. At times I just give up and wait for an hour or more in case the carburetor is flooded. All in all it is a frustrating experience and not what it should be.

So I came up with the idea shown in the video. It's just a simple way of directly feeding starting fluid directly into the engine carburetor. What this means is you don't have to remove the filter cover and the filter to get a good spray of starting fluid directly into the carburetor. Watch the video first and then check out the photos for extra info and the procedure to start the engine once you make the modification.

For my generator I had to remove a corner of a plastic plate behind the air filter so that the installed feed tube will allow a direct spray to the carburetor input. I removed the corner with first a small pilot hole drill and then a larger drill. Be sure to close the carburetor valve when drilling to keep any loose particles from getting in. Also make sure you clean out all plastic particles left from the drilling.

To make a tight fitting hole for the nipple in the air filter I ended up using a small carving chisel. (First I tried to make the hole with a twist drill but the filter material just wound up around the drill.)

The awl, fed though the feed tube (nipple), is a quick way to mark the location of the required hole in the filter cover. Once the hole center is marked the hole can be drilled and the feed tube mounted with an inside nut and lock washer and an outside locking nut.

After assembly of the filter and cover (feed tube already installed) you can carefully fit the assembly back in place on the mating carburetor frame. This might take a little bit of feeling around as now the filter is mounted on the cover where normally it is separate and installed first. To clue up before testing, lock the cover in place with the top and bottom clips and test fit the feed tube cap.

Note: I had to search around a bit to find a spray can nozzle and extension tube to fit my can of starting fluid. Now I think that the best approach is to find a longer nipple (at least 3 inches) so that a nozzle extension is not then needed. Bottom line is you don't want a plastic extension tube popping off and getting into the carburetor.

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.

The Integral Calculator supports definite and indefinite integrals (antiderivatives) as well as integrating functions with many variables. You can also check your answers! Interactive graphs/plots help visualize and better understand the functions.

Enter the function you want to integrate into the Integral Calculator. Skip the f(x)= part and the differential dx! The Integral Calculator will show you a graphical version of your input while you type. Make sure that it shows exactly what you want. Use parentheses, if necessary, e.g. a/(b+c). Write decimal fractions with a period instead of a comma, e.g. 3.141.

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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.

The parser is implemented in JavaScript, based on the Shunting-yard algorithm, and can run directly in the browser. This allows for quick feedback while typing by transforming the tree into LaTeX code. MathJax takes care of displaying it in the browser.

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. In many cases, 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.

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.

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