Bioeng 376 / Bioph 317 / Neuro 317 /Physl 317
Outline - Lecture 1
M. Nelson  Spring 2004

Basic Tools

A neural modeler needs to have a handy set of tools from math, physics, computer science, and neurobiology. Here's a review of a few of the things that should be in your basic toolbox.  If some of your tools are rusty, it's time to get them oiled up and ready to go.

trig functions	basic properties of sin, cos, tan, ... relationship between degrees and radians (180deg = pi radians) geometrical interpretation (e.g., cosine = adjacent/hypotenuse) relationships: sin2 + cos2 = 1, tan(a) = sin(a)/cos(a), etc.
exponentials & logarithms	basic properties of exponentials, e0 = 1, e1 ~ 2.71818, etc. sketch exponential decay curve, exponential charging curve graphically identify time constant, 1/e ~ 37% identify time constant from equation properties of logs,  log(0) = -infinity, log(1) = 0, ln(e) = 1, etc. choice of base-10, base-2, natural log, etc. convert from one base to another semilog, loglog plots
derivatives	differentiate terms containing polynomials, trig functions, exponentials chain rule, product rule, quotient rule, etc. Differentiation Review Page Differentiation Examples
integrals	integrate expressions of polynomials, trig functions, exponential Table of Integrals
vectors & matrices	row and column vectors, transpose operator identity matrix matrix multiplication dot products, cross products Brief linear algebra review (PDF)
ordinary differential equations	differential equations as models temporal derivatives as rate-of-change ability to integrate simple cases by hand numerical integration, Euler's method initial value specification (where to start) steady-state solutions Euler's Method
basic electrical circuit analysis	Kirchoff's current law (current conseration at nodes) Kirchoff's voltage law (sum of voltage drops around a loop is zero) Ohm's law: V = I R Conductance is inverse resistance g = 1/R; Ohm's law: I = gV Capacitance: q = CV Capacitive current: I = dq/dt = C dV/dt RC circuit, RC time constant Analysis of Resistive Circuits