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https://github.com/cleoold/calculus-toolbox

a toolkit available to calculate various expressions in calculus.
https://github.com/cleoold/calculus-toolbox

calculus math racket scheme

Last synced: about 2 months ago
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a toolkit available to calculate various expressions in calculus.

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With this tool, you can do math and engineering calculations, such as integrals, recurrence sequences and vectors, more easily.


All you need to do are to stick with some function syntax in Scheme (like using brackets ()) to enter formulas, and put integers


to select things in my menu.


The repository containing the source codes is located page. The programme is written in Scheme, you can


open the file runme.scm in the main folder in Drracket to run it (as it includes #lang scheme prefix). If you are using a different


interpreter or compiler, you might need the corresponding module and comment out that #.




Library



The executable embeds all the necessary dll's in the single file. It includes the math library also. So this tool supports various


operators like (+ x y z), (- x y), (* x y), (/ x y), (sin x), (cos x), (tan x), (asin x), (acos x), (atan x), (sinh x), (cosh x), (tanh x), (sqrt x), (log x), (exp x), (floor x), (ceiling x). Especially, x^3 is converted to (expt x 3).


The tool itself provides a documentation about conversion of equation formats. For example,  is converted into (* 1.5 (cos (+ (* w t) (-1 k x) (/ pi 2)) ) ).


Using



In Linux, open the terminal and navigate to /bin, use command ./calculus-tool to open the executable.


Under the calculus-toolbox/standalone-executables/ folder, you can find the standalone executable files that can be run on Linux and Windows.




Instruction



Below describes the features of this tool.


Solving equation



In the main menu, enter 1 to navigate to calculus menu, and then hit another 1 to arrive here.


In this screen, type your function and be sure to include the variable x only. For example, to solve x^3 - e^x + 3 = 0, you need to


type (+ (expt x 3) (- (exp x)) 3), then hit enter. Since the tool uses Newton's method to evaluate, it will then ask you for an initial


guess, type any number you think will be close to a solution. For precision, you can input 0.001 or other small numbers; the tool


uses this to find the derivative. The next step is to determine how many resursive calls it will evaluate the root, since the sequence   converges fast, you don't need to input a number that's too large.


The tool will print a solution after you hit enter, or reports an error if the input format is not correct.


⋅⋅⋅solve12


You can later change your initial guess to find other solutions.


The programme will remember the input data from the last state in which it is run.


Derivative



In this screen, also make sure include the variable x; this programme doesn't support other variables as input. You can input your desired point and precison. Note this precision represents the term h in the formula . The result after evaluation will be then printed.


If you also want the left derivative, you can go to the additional menu to do the exact same steps, which is useful for determining


whether the derivative exists.


After the update on April 2019, a second derivative feature is added.


Integration



Like others, you have to include x and syntax. You will be asked to input the lower bound (from), the upper bound (to) and precision.


Note this precision "delta" represents the length of the step  for the partition. This tool creates


a uniform partition with that length (if delta cannot divide the length of the interval, a shorter interval is created to terminate the programme, please see code for info) and sum the average values of two ends of the subinterval according to the midpoint rule. This process can be described as





In which the term on the right can be avoided upon decreasing value of precision, or by using rational bounds.


If you want to evaluate the left or right integral, you can go to the additional menu to do so. This is useful for determining if


the integral exists; if the programme crashes, then it is not integrable over the interval.


Recurrence sequence



If a sequence is determined recursively, then this tool provides great help for building a table and summing terms.


Before using, please acknowdge that the index of a sequence starts from 0. if a term is determined recursively by its previous


term, then it needs one base value. Such sequences look like  . In this case, enter 1. If a term is determined by two of its previous values, then it needs two base values, and (possibly) looks like


. For this, enter 2.


Now you can enter your A, and B if necessary. In the next step, if you entered 1, then include x in your expression. That x represents the last term based on generating the new term. If you entered 2, then use x for , and y for .


You can then input your order to evaluate things, below shows a sequence defined by .


⋅⋅⋅4211245


Gradient



This menu calculates partial derivative, gradient, and directional derivative for a function defined by multiple variables.


To start, enter your list of variables enclosed by brackets in the first screen, then input the function that has these variables.


For example, for , you need to enter (x y z) first, then (expt (* x y z) 1/3) second. The program will turn it into a


lambda expression for that expression.


Now for each of the three features, you need to input points (or vectors). For example, if you want to type in a point (2 5 2.2),


then simply type in (2 5 2.2) for that. Also, they need the precision input, this is the same as in the previous derivative section.


Below shows a calculation for directional derivative at (2 3 9.2), followed by the gradient.


523t3


Decimal conversion



This tool in under the additional menu. You can do the conversion from decimal to baseN (N >= 2), or from baseN to decimal


(1 <= N < 10). The algorithm can be found here.


⋅⋅⋅53243


Product of vector



You can find this option under the vector menu. You can input your vector u first, followed by v. The tool will compute their dot


product for you, and if the length is 3, then it also returns the vector u × v.


⋅⋅⋅42523


Projection



This feature produces three vectors at once upon you inputting two vectors. After you enter x first and then u, the followings are returned in order:


    

  1. Projection of vector x onto vector u. 

    2. 

  2. Perpendicular of vector x onto vector u. 

    3. 

  3. reflection of vector x onto the hyperplane with normal u. 

    4. 



And more minor tools



Updates will be on page. The tool also provides vector rotation, vector molulo, sum/product of sequence and more.




Progress



I give up on vector addition, hexadecimal conversion, building function table, etc as they are less challenging and can be found anywhere on-line or on your scientific calculator. In the future, I will plan to implement approximations of double integral, and some matrix operations such as multiplication and determinants.