We've had our hardwood floors refinished and had to move the office library out and back. In the move I came across a collection of text books from grad school. Several were on Real Analysis, better known as real number calculus. A quick glance through them during reshelving triggered a thought - OK it's a bit of a stretch I know. There is a *calculus* of project management similar to the calculus of real analysis.

Calculus has two basic ingredients - differentiation and integration. Differentiation is concerned with velocities, accelerations, curvature, and surfaces among other things. These are "rates of change," they are quantities defined *locally* in terms of neighborhoods around a single point.

Integration is concerned with areas, volumes and things that involve measures of totality.

Each is defined as the *inverse* of each other.

How in the world does this pertain to Project Management?

- Differentiation - normative and rational aspects of project management. Local rules, rates of change, measurements of performance, changes in direction, local measurements, inward focused.
- Integration - broad sweeps of concern, averages, smoothing of surfaces.

There is a striking difference between differentiation and integration. Differentiation is considered "easy." Operations can be applied to formula involving known functions - rules, algorithms, normative outcomes. Integration is much harder (except for numerical tabular data). Rules are not clear and concise - although there are numerous example of how to integrate a function - there is no "simple" algorithm like there is in differentiation.

The differentiation rules are like the normative and rational rules of PMBOK and traditional project management. The integration processes are like the participative and heuristic processes of agile project management. With me so far?

The critical concept is they are both required to solve problems, one without the other leaves the problem without sufficient tools to be solved.