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====== Math 445: final exam topics ====== Material to be covered on the final falls into three categories corresponding to three phases o * matlab basics (exam 1 content) * functions, scripts, plotting, Newton solve, Monte Carlo methods (exam 2 topics) * 3D graphics and numerical integration of differential equations (material since exam 2) ===== Matlab basics ===== You should know the basic Matlab functionality for * Arithmetic operations * Writing mathematical expressions in Matlab with arithmetic operators ''- + * / ^'' * Assignment into variables with ''=''. * How to enter numbers in scientific notation; e.g. ''3.2e-04'' means $3.2 \times 10^{-4}$. * How to enter complex numbers, e.g. ''4 + 5*i''. * Logical expressions (which evaluate to true or false) * how Matlab represents true with 1 and false with 0 * comparison operators ''< > <= >= == ~='', e.g. ''3 < 2'' has value false, or 0 * logical operators ''&& || xor ~'' * how to combine all these to make logical expressions, e.g. ''3 < 2 || 4 > 1'' has value true, or 1 * Vectors and matrices * square bracket notation for creating row vectors, column vectors, matrices * when to use commas (separating elements in a row), when to use semicolons (marking end of row) * creating vectors with ''linspace'' and colon syntax, e.g. ''x = 0:0.01:4'' * creating vectors and matrices with ''zeros, rand, randn'' * matrix-vector multiplication, the definition and meaning * ''Ax=b'' problems, forming them from story problems or equations and solving in Matlab with ''\'' * accessing/setting elements, e.g. ''A(:,3)'' is the 3rd column of ''A'' * linear algebra operations: ''+ - * \ ^ ' '' * elementwise operations: ''- + .* ./ .^'' * matrix-vector input/output: ''load/save'' * Plotting * making plots with ''plot, semilogy, semilogx, loglog'' * making plots with multiple graphs, colored, dashed, dot-dashed etc. lines, symbol markers * annotation: ''xlabel, ylabel, title, grid on, legend, axis, clf, legend, hold on, hold off'' * graphical data analysis * ''plot'' for ''y = mx + b'' * ''semilogy'' for ''y = c 10^(mx)'' * ''semilogx'' for ''y = m log x + b'' * ''loglog'' for ''y = c x^m''
