Engineer searching for calculus and complex analysis books without limits I am an engineer and I need to study calculus and complex analysis without too much limits or Riemann sums or proofs. I mean on the differentiation and integration levels and higher (not digging downwards for proofs), with emphasis on geometric and physical interpretations (meanings) and applications. What books do you suggest? 
By the way I heard that calculus and infinitesimals where used before the formal precise definition was invented latter. Does a book of that era can help me?
Thanks in advance.
 A: It's almost impossible to avoid limits if you want to do anything meaningful in complex analysis.
For one, the notion of differentiability in complex analysis is, although conceptually equivalent, mechanically different when analyzing complex functions. There's not really a notion of "symbolic differentiation." For example, take an arbitrary polynomial $P(z)$ in $\mathbb{C}$. This polynomial is almost surely not differentiable in $\mathbb{C}$. Functions in $\mathbb{C}$ that are differentiable are also analytic and holomorphic. These are important concepts; at least with analyticity, you get a real-valued analogue in that an analytic function has a Taylor series that converges.
Likewise, integration takes on a somewhat different meaning. In $\mathbb{C}$, we concern ourselves predominantly with contour integration. Functions in $\mathbb{C}$ become interesting to integrate when they have singularities, i.e. they are analytic everywhere except at some number of points. Contour integration serves as the fundamental basis for the interesting engineering applications pf complex analysis: the Fourier transform and the Laplace transform, for instance, are just contour integrals.
However, it's nearly impossible to approach these ideas mechanically. The important theorems all involve convergence of infinite sums and limits. Arguably the most powerful contour integration tool, the Residue Theorem, states that a contour integral of a function analytic everywhere on a domain except at poles is equal to the sum of the residues on those poles. And residues themselves are defined as limits! We cannot get away from this concept.
The basic cases that you may encounter in traditional engineering applications are summarized nicely in Shaum's Outline of Complex Variables. But you won't really understand the field; at best, you'll simply memorize a technique that only works for a handful of toy problems.
