1Systems of Eqs and Vector Math2/11/20082Opening Discussion■What did we talk about last class?■Do you have any questions about the reading?■Do you have any questions about the assignment?3Fitting Data as a Linear Eq■The process of fitting data points to a linear combination of functions can be viewed as solving a system of linear equations.■Given points (x1,y1)...(xn,yn) and functions f1(x)...fn(x) we fill in the A matrix with Aij=fj(xi) and let the y values be the y vector. Solving gives us the proper coefficients.■If it is overdetermined this process will give us the values from a least-squares fit.4Non-Linear Equations■What if you want to do something like perform an exponential fit?■In general we'd have to do a different procedure with non-linear optimization.■If the fitting function isn't too complex though you can sometimes convert it to a linear form using a bit of algebra.5Physics and Vectors■With the time remaining lets talk about some concepts of N-body simulations and how they would appear in Matlab.■N-body simulations involve a number of discrete particles. These particles feel various forces.■The locations, velocities, and forces are all represented as vectors. In Matlab these can be just arrays and the language simplifies how we express the math.6Closing Remarks■Quiz #2 is next
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