This classic paper covers what can be called the 'Differential' method. This requires the assumption of 'small error.' In real situations you might not be able to justify this or in multiple calculations, the error grows, invalidating the original assumption. Other problems with this approach are the 'dependency problem,' the failure of divide by zero with error and square root of zero with error.
I have developed new methods based on geometric arithmetic that do not rely on the small error assumption. These methods are capable of 'divide by zero with error' and 'square root of zero with error.' If you want to learn more about this, visit CertainError.com . I have listed many recent projects (Industries tab) I have examined.
In addition, I have develop apps (for Apple and Android) that perform automatic error propagation for a variety of methods (Differential, Intervals, Monte-Carlo, Chordals, Duals). The idea is to replace scientific calculators with the CertainError Calculator when error propagation is required.
This calculator is being used to enhance the instruction of error propagation and uncertainty analysis in beginning or freshman level courses, before the students have solid knowledge of partial differentiation and statistics. There are many students on the international stage that would benefit from this. You can contact me about this through the CertainError.com website or by email [email protected].