What are some applications for engineering that uses Taylor series?
The Taylor series is mostly obsolete in engineering applications. It is an introductory method to give students an idea that such a concept of infinite series converging to a hard-to-calculate function does exist. And the Taylor series is easy to understand its origin and motivation. There are much more effective methods (achieving greater accuracy for each computation step) available for calculating exponential, logarithms, and trigonometry than the Taylor series.