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Numerical integration for novices

January 2, 2012

Numerical integration is an essential technique in computational neuroscience. Does that mean a student can’t do computational neuroscience without taking a course on differential equations? Certainly a formal course would help, but I think there is an alternative for learning how to work with something like the Hodgkin-Huxley model. I’ve had undergrads who wanted to work on neuronal simulations but had not yet had a course on differential equations or numerical methods. They have all been capable of understanding what the equations mean without knowing much about the theory. To deal with this, I put together a Crash Course on Numerical Integration. It uses an example from physics for the height of a falling object, which is something most students have seen before.

Generally, I believe the most effective way to teach is to build strong bridges from a student’s existing knowledge that connect with the new knowledge. Interestingly, I have found that most students are very capable of grasping the fundamentals of numerical integration as long as they have two prerequisites: (1) some exposure to calculus, and (2) a basic knowledge of computer programming. Luckily most freshman get both of these by the end of their first year in college.

The relevance of calculus is obvious, but how does a knowledge of computer programming help? I believe the experience of writing a loop in a computer program provides a very important bridge to understanding numerical methods. The way that the value of a variable changes inside a loop is remarkably similar to how state variables change in numerical integration. Because of this, my Crash Course uses this idea of repetition to create a bridge to the idea of integration. I have only recently started to use this approach for students interested computational neuroscience. It remains to be seen whether it can really provide a bridge to working effectively with something as complex as the Hodgkin-Huxley model.

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