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gibson:teaching:fall-2016:math753:finalexam [2016/12/12 18:33]
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gibson:teaching:fall-2016:math753:finalexam [2016/12/12 19:00] (current)
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    * Horner'​s method: be able to rearrange a polynomial into Horner'​s form, and understand why you'd do that    * Horner'​s method: be able to rearrange a polynomial into Horner'​s form, and understand why you'd do that
    * Lagrange interpolating polynomial: be able to write down the Lagrange interpolating polynomial passing through a set of data points $x_i, y_i$, and understand why the formula works    * Lagrange interpolating polynomial: be able to write down the Lagrange interpolating polynomial passing through a set of data points $x_i, y_i$, and understand why the formula works
-   ​* ​+   ​* ​Newton divided differences:​ know how to use this technique to find the interpolating polynomial through a set of data points $x_i, y_i$ 
 +   * Chebyshev points: what are they, what are they good for, why do we need them? 
 + 
 +Least-squares models 
 +   * Understand how to set up least-squares $Ax=b$ problems to find the best fit for functions of the following forms to $m$ pairs of datapoints $t_i, y_i$ 
 +       * an $n$th order polynomial  
 +       * an exponential $y=c e^{at}$  
 +       * a power law $y=c t^a$  
 +       * a curve of the form $y = c t e^{at}$  
 + 
 +Finite differencing and quadrature 
 +    * be able to approximate the first & second derivatives of a function $y(x)$ from the values $y_i = y(x_i)$ where the $x_i$ are evenly spaced gridpoints $x_i = x_0 + i h$ 
 +    * provide error estimates of those approximate derivatives 
 +    * be able to approximate the integral $\int_a^b y(x) dx$ of the function $y(x)$ from evenly space gridpoint values $y_i = y(x_i)$, using the Trapeziod Rule and Simpson'​s rule 
 +    * provide error estimates for those approximate integrals 
 + 
 +Ordinary differential equations 
 +    * what is an initial value problem? 
 +    * why do we need to solve initial value problems numerically?​ 
 +    * what are the timestepping formulae for  
 +        * Forward Euler 
 +        * Midpoint Method (a.k.a. 2nd order Runge-Kutta) 
 +        * 4th-order Runge-Kutta 
 +        * Backwards Euler 
 +        * Adams-Moulton 
 +    * what are the global error estimates of the above timestepping formulae? 
 +    * what is a global error estimate versus a local error estimate, and how are the two related? 
 +    * what's the difference between an explicit method and an implicit method? 
 +    * what's a stiff differential equation? what kind of method do you use for a stiff  equation? 
 +    * how do you convert an $n$th order differential equation in one variable to a system of first order differential equations in $n$ variables?​ 
 + 
  
  
  
  
gibson/teaching/fall-2016/math753/finalexam.txt · Last modified: 2016/12/12 19:00 by gibson