To develop a GUI calculator application, utilizing existing libraries or language features like 'eval' can simplify the process of evaluating mathematical expressions. For those interested in understanding expression parsing, resources such as lex and yacc are recommended. Specifically for MATLAB, the focus should be on using its GUI library to construct strings representing mathematical operations, which can then be processed using MATLAB's eval function. This approach allows for the implementation of basic operations such as addition, subtraction, multiplication, and division without needing to create a complex algorithm from scratch.