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gibson:teaching:spring-2018:math445:finaltopics

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====== Math 445 final exam topics ====== The final exam will likely have * 10 problems on matlab (similar to exam 1 questions) * 5 problems on labs * 2 essay questions about your experience with labs and lecture ====Matlab topics==== 1. creating and manipulating vectors and matrices * colon operator: creating vectors of integers, over a range and with a given increment * accessing elements of vectors * accessing rows, cols, and elements of matrices * determining the size of vectors and matrices * dot syntax for elementwise operations versus linear algebra operations 2. linear algebra * matrix-vector multiplication * mathematical definition * computing numerical examples on pencil and paper * computing numerical examples in matlab * converting story problems to Ax=b problems * solving Ax=b problems in Matlab 3. evaluating complex mathematical expressions in Matlab * e.g. $\sum_n=1^7 n^2/(n+4)^2$ with 'sum' 4. xy plots * creating 1d grid with linspace (or logspace) * evaluating expressions over 1d grids using dot syntax * plot command: plot y versus x, specify colors and line styles * labeling axes, titles, grid, legend * semilogy, semilogx, loglog - what kind of functional relationships each is appropriate for - estimating functional relationships from graphs of each 5. writing simple functions in Matlab * syntax for function in a file * syntax for anonymous function * functions involving for loops (e.g. matrix-vector mult) 6. 3d graphics * creating 2d grids of coordinates with meshgrid * evaluating functions on 2d grid with dot syntax * Matlab functions 'plot3 contour, contourf, surf, quiver' ====Labs==== 7. hamster dynamics / Google Page rank * derive a transition matrix $x^{n+1} = A x^n$ from a network of links * write code to iterate $x^{n+1} = A x^n$ 8. nonlinear equations $f(x) = 0$ * know Newton iteration equation $x_{n+1} = x_n - f(x_n)/f'(x_n)$ * derive Newton iteration equation graphically or from Taylor series * write function that uses Newton iteration to find solution of $f(x) = 0$ for given function $f$ and initial guess $x_0$ 8. differential equations: given a system of differential equations $dx/dt = f(x)$ for vector $x$, write * code for the function $f$ which computes $dx/dt = f(x)$ * code that integrates $dx/dt = f(x)$ numerically using ode45 * code that plots the solution of the numerical integration * code that draws quiver pliot for vector field $dx/dt$

gibson/teaching/spring-2018/math445/finaltopics.1525371004.txt.gz · Last modified: 2018/05/03 11:10 by gibson