In my experience, many introductory engineering mathematics textbooks these days tend to skip proofs and discuss logic only in the context of digital electronics. On the other hand, I can imagine that engineers (and others) could benefit from developing basic skills in mathematical thinking* beyond the cookbook approach. (See, for instance, Keith Devlin's Introduction to Mathematical Thinking course.) I hasten to add that many engineering mathematics textbooks do have strong points, such as numerous examples of mathematics applied to solving engineering problems.
I would be very interested in learning about either engineering mathematics textbooks that do contain material on mathematical thinking or your experience(s) in teaching introductory mathematics to engineers where you went beyond the cookbook approach. Input from engineering students and practising engineers is also welcome, as are contributions from those involved in other fields in which mathematics is applied.
(For the record, I currently use Engineering Mathematics: A Foundation for Electronic, Electrical, Communications and System Engineers by Croft et al. The material covered includes derivatives, integrals, complex numbers, matrices, differential equations, Laplace transforms and Fourier series.)
- I realize that I haven't defined mathematical thinking. Keith Devlin addresses this in his blog entry What is mathematical thinking? See also Terry Tao's There's more to mathematics than rigour and proofs and the anonymous answer to the question What is it like to understand advanced mathematics? However, please note that I am focusing on introductory courses and basic skills in this question.