the first few steps you try to run the program to see what python' response is then you know what the problem is and understand what the error message is about this will greatly help you when you get similar error message or warning later very oftenyou will experience that there are errors in the program you have written this is normalbut frustrating in the beginning you then have to find the problemtry to fix itand then run the program again typicallyyou fix one error just to experience that another error is waiting around the corner howeverafter some time you start to avoid the most common beginner' errorsand things run more smoothly the process of finding and fixing errorscalled debuggingis very important to learn there are different ways of doing it too special program (debuggermay be used to help you check (and dodifferent things in the program you need to fix simpler procedurethat often brings you long wayis to print information to the screen from different places in the program first of allthis is something you should do (several timesduring program development anywayso that things get checked as you go along howeverif the final program still ends up with error messagesyou may save copy of itand do some testing on the copy useful testing may then be to removee the latter half of the program (by inserting comment signs #)and insert print commands at clever places to see what is the case when the first half looks okinsert parts of what was removed and repeat the process with the new code using simple numbers and doing this in parallel with hand calculations on piece of paper (for comparisonis often very good idea python also offers means to detect and handle errors by the program itselfthe programmer must then foresee (when writing the codethat there is potential for error at some particular point iffor examplesome user of the program is asked (by the running programto provide numberand intends to give the number but instead writes the word fivethe program could run into trouble try-exception construction may be used by the programmer to check for such errors and act appropriately (see for an example)avoiding program crash this procedure of trying an action and then recovering from troubleif necessaryis referred to as exception handling and is the modern way of dealing with errors in program when program finally runs without error messagesit might be tempting to think that ah am finishedbut nothen comes program testingyou need to verify that the program does the computations as planned this is almost an art and may take more time than to develop the programbut the program is useless unless you have much evidence showing that the computations are correct alsohaving set of (automatictests saves huge amounts of time when you further develop the program verification versus validation verification is importantbut validation is equally important it is great if your program can do the calculations according to the planbut is it the right planput otherwiseyou need to check that the computations run correctly according to the formula you have chosen/derived this is verificationdoing the things right thereafteryou must also check whether the formula you have chosen/derived is the right formula for the case you are investigating this is validationdoing the right things in the present bookit is beyond scope to question how well the mathematical models describe given phenomenon in nature or engineering