As a mathematics textbook it of course provides rigorous proofs. But it doesn't ...

As a mathematics textbook it of course provides rigorous proofs. But it doesn't neglect to develop intuitive insight (that can be less rigorous yet still very effective).

Here's a quote given in chapter two. That's some motivation to develop more mathematical maturity as an engineer!

  In 1985, John Hubbard was asked to testify before the
  Committee on Science and Technology of the U.S. House of
  Representatives. He was preceded by a chemist from DuPont,
  who spoke of modeling molecules, and by an official from the
  geophysics institute of California, who spoke of exploring
  for oil and attempting to predict tsunamis. When it was his
  turn, he explained that when chemists model molecules, they
  are solving Schrödinger’s equation, that exploring for oil
  requires solving the Gelfand-Levitan equation, and that
  predicting tsunamis means solving the Navier-Stokes equation.
  Astounded, the chairman of the committee interrupted him and
  turned to the previous speakers. “Is that true, what
  Professor Hubbard says?” he demanded. “Is it true that what
  you do is _solve equations_?”