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The guiding principles are behavioral in the catholic sense of that word, but with a special emphasis not simply on the structure of the phenomena observed but on their function -- what they do or affect in a dynamic system. Gather additional information based on Step 2 and finalize the conceptual analysis.

Course Features

As features of the case coalesce, additional information is gathered relevant to the analysis. Specific assessment devices may be selected or created to examine particular features of the case as conceptualized in Step 2.

In this process, the analysis may be refined and modified. Eventually the assessor has a stable conceptual analysis of the relation between actions of the client and its context, with measurement data on the primary components of that analysis and assessment procedures in place for a continuing evaluation of the case. Devise an intervention based on Step 3.

How is this practical?

One dominant characteristic of behavioral assessment is the close link, at least conceptually if not often empirically, between assessment and treatment. Because behavioral principles are explicitly pragmatic their confirmation is usually based on the ability to predict and influence behavioral events through their use , a functional analysis often points to concrete events in the life of the clients that have established and are maintaining the problem of interest. If these events are manipulable in the practical world of clinical intervention, a thorough-going functional analysis often directly suggests a particular intervention.

Thus, in Step 4 a treatment is devised that is linked to Step 3. Implement treatment and assess change. Assessment, to most behavioral assessors, is not something done only at the beginning of treatment. It is an ongoing process. Thus, a functional analysis contains within it the ongoing assessment of clients' progress. If the outcome is unacceptable, recycle back to Step 2 or 3.

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If treatment is not successful, usually this is taken as an indication that the conceptualization phase of the functional analysis itself is flawed. Thus, a failure to see the kinds of changes that are desired leads directly to a reexamination of the conceptualization, either in the form of a minor adjustment or, at times, a complete overhaul of the analysis. Finite element methods, for example, are easier to understand in the context of functional analysis. You formulate your problem in some infinite dimensional function space, usually a Sobolev space , and project it down to a finite dimensional approximation in terms of functions on finite elements.

The modern approach to working with partial differential equations, whether in theory or in computation, is usually framed in terms of functional analysis. The same is true of optimization. All of this is justified using functional analysis.

Department of Mathematics

When you have a norm on a function space, i. You can do things like taking derivatives where your variables represent functions rather than points in space.

Functional analysis is critical in understanding when you can proceed on analogy with ordinary calculus and when you have to be more careful. For help applying the tools of functional analysis to your problems, please call or email to discuss your project.

How is this practical? Applications There are many applications of functional analysis to differential equations.