gibson:teaching:spring-2015:math445:finaltopics
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gibson:teaching:spring-2015:math445:finaltopics [2015/05/01 13:28] gibson |
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| ====== Math 445: final exam topics ====== | ====== Math 445: final exam topics ====== | ||
| - | a work in progress ... expect content over the weekend of May 2nd & 3rd ... until then, | ||
| - | * matlab basics (exam 1 content) | + | ===== Matlab basics ===== |
| - | * functions, scripts, plotting, Newton solve, Monte Carlo methods (exam 2 topics) | + | |
| - | * 3D graphics and numerical integration of differential equations (material since exam 2) | + | 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 ~'' (and, or, exclusive or, not) | ||
| + | * 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 functions of one variable | ||
| + | * making plots of 1d functions $f(x)$ 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: be able to determine ''y'' as a function of ''x'' from a plot | ||
| + | * ''plot'' for ''y = mx + b'' | ||
| + | * ''semilogy'' for ''y = c 10^(mx)'' | ||
| + | * ''semilogx'' for ''y = m log x + b'' | ||
| + | * ''loglog'' for ''y = c x^m'' | ||
| + | * Plotting functions of two variables | ||
| + | * creating ''X,Y'' matrices with ''meshgrid'' | ||
| + | * plotting functions of two variables with ''pcolor, contour, contourf, surf, surfc, quiver'' | ||
| + | * changing colors with ''colormap'' | ||
| + | * displaying color scale with ''colorbar'' | ||
| + | |||
| + | |||
| + | ===== Matlab programming: functions, scripts, loops ===== | ||
| + | |||
| + | You should be able to write short Matlab programs to perform specified computations. | ||
| + | * how to write a function in a file with ''.m'' extension | ||
| + | * how to write an anonymous function, e.g. ''f(x) = @(x) x^2 - 3*x + 2'' | ||
| + | * how to write a ''for'' loop to evaluate a sum or product | ||
| + | * how to write a ''for'' loop to perform a repeated computation | ||
| + | |||
| + | ===== Lab material ===== | ||
| + | |||
| + | You should have a good grasp of the underlying mathematics and implementation in Matlab code of these labs, i.e. how to ... | ||
| + | |||
| + | * [[gibson:teaching:spring-2015:math445:lab3]] solve a set of linear equations ''Ax=b'' with Matlab's backslash operator | ||
| + | * [[gibson:teaching:spring-2015:math445:lab7]] solve a nonlinear equation $f(x) = 0$ by coding ''f'' as an anonymous function and calling Matlab's ''fsolve'' function. | ||
| + | * [[gibson:teaching:spring-2015:math445:lab8]] determine a transition matrix from a network of links and compute the Google Page Rank. | ||
| + | * [[gibson:teaching:spring-2015:math445:lab9]] simulate uncertain systems like coin flips and Presidential elections with Monte Carlo simulation. | ||
| + | * [[gibson:teaching:spring-2015:math445:lab11]], [[gibson:teaching:spring-2015:math445:lab11]], [[gibson:teaching:spring-2015:math445:hw3]] do numerical integration of differential equations with ''ode45'' | ||
| + | |||
gibson/teaching/spring-2015/math445/finaltopics.1430512114.txt.gz · Last modified: 2015/05/01 13:28 by gibson
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