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Contour Integral or Complex Path Integral

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Let's find contour integral of 1/Z where path of Z is a circle on complex plane. First, we need to define expression for the circle using a separate parameter variable T and add it to our CAL list. The expression should define both real and imaginary parts of the complex path. So, we input the complex expression cos(T) + i * sin(T) and add it to the CAL list using the AddToList option. (Use the F1 option to add cos and sin functions and VAR option to add parameter var T) After saving the expression for the path to CAL list, we clear the current expression box and enter the expression 1/Z and tap ≈∫ to integrate it with respect to var Z. Select var Z as our integral var. By default, the app assumes the path of var to be real. Since we know that Z is a complex path, we select the option "Is var below complex?" and tap on "Complex Path..." to define the path of Z on complex plane. We use the saved expression for complex path from the CAL list and specify parameter
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Plot or Integrate using simulated data in specified range

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To plot or integrate, input expression with respect to an independent variable and then tap ðŸ“ˆ or ≈∫ For example input expression X * X  + X where X is an independent variable. Tap on  ≈∫ , select independent variable as X and start-end range from -5 to 5 Result  -5 5 ∫  Æ’ dX = 83.333333333 (Approx) Note1: The range for integral (end - start) has a limit that is shown by the app. Note2: The result of plot or integral may be inaccurate for expressions with very high frequency. To avoid such errors the displayed sampling rate should be kept many times the frequency of expression. The user can increase the sampling rate by decreasing the start-end range.
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Plot or integrate using file spreadsheet data

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Use  the "Var=> ▤ Values=>Read from Sheet" option to open the  variable  editor . Then read from a spreadsheet file using the "Read Create Spreadsheet..." option. After the file is read by the app, a page is displayed showing the variable names from 'A' to 'Z' where each variable is mapped to a specific column.  If required, change the default mappings. You may specifically want to change mapping for an independent variable like X to point to a column having independent values. This column can be used as a reference to plot or integrate. (Skip this step if there is no independent variable for example in case of sequential data) By default, Variable X is mapped to 1st column. Y is mapped to 2nd column. To plot or integrate 2nd column data in file with respect to 1st column, simply input the expression Y and tap on  📈 or ≈∫ and select independent variable as X.  The data/rows will be automatically sorted with respect to X column by the app. If y
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