gibson:teaching:spring-2016:math445:finaltopics
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gibson:teaching:spring-2016:math445:finaltopics [2016/05/16 06:11] gibson |
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| ====== Math 445 final exam topics ====== | ====== Math 445 final exam topics ====== | ||
| - | The Math 445 final exam will be comprehensive, covering all material presented in lecture and lab (except for the derivation of differential equations from physics presented in lecture). | + | The Math 445 final exam will be comprehensive, covering all material presented in lecture and lab (except for the derivation of differential equations from physics presented in lecture). Below is a broad overview but not exhaustive of topics that might be covered on the exam. |
| ---- | ---- | ||
| + | ===== Matlab syntax ===== | ||
| + | |||
| ====Vectors and matrices==== | ====Vectors and matrices==== | ||
| Line 54: | Line 56: | ||
| You should know | You should know | ||
| * how to make $xy$-plots of given functions $y=f(x)$ using **linspace**, elementwise operations on vectors, **plot**, **semilogx**, **semilogy**, and **loglog**. | * how to make $xy$-plots of given functions $y=f(x)$ using **linspace**, elementwise operations on vectors, **plot**, **semilogx**, **semilogy**, and **loglog**. | ||
| - | * how to make 2D contour plots with **linspace**, **meshgrid**, elementwise matrix operations, and **contour** or **contourf** | + | * how to make 2D color plots with **pcolor**, using **linspace**, **meshgrid**, elementwise matrix operations as well |
| - | * how to make 3D surface plots with **linspace**, **meshgrid**, elementwise matrix operations, and **surf** | + | * how to make 2D contour plots with **contourf** and **linspace**, **meshgrid** etc. |
| + | * how to make 2D quiver plots with **quiver** and **linspace**, **meshgrid** etc. | ||
| + | * how to make 3D surface plots with **surf** and **linspace**, **meshgrid**, etc. | ||
| * how to load data from a file and plot it | * how to load data from a file and plot it | ||
| * how to label axes, title a plot, color the lines, show markers on data points, display a coordinate grid, show a colorbar, etc. | * how to label axes, title a plot, color the lines, show markers on data points, display a coordinate grid, show a colorbar, etc. | ||
| ---- | ---- | ||
| - | ==== Log-linear relations ==== | ||
| - | You should know how to infer a functional relation $y=f(x)$ given a logarithmic or linear plot | ||
| - | , and which of **plot**, **semilogx**, **semilogy**, and **loglog** is best for a given relation $y=f(x)$. | ||
| - | |||
| - | ---- | ||
| ==== Evaluating expressions ==== | ==== Evaluating expressions ==== | ||
| Line 116: | Line 115: | ||
| ---- | ---- | ||
| + | ==== random numbers ==== | ||
| + | |||
| + | You should know how to get random numbers of various kinds | ||
| + | |||
| + | * **rand**: a random floating-point number between 0 and 1. | ||
| + | * **randi(max)**: a random integer between 1 and max. | ||
| + | * **randn**: a random number in a Gaussian distribution with mean 0 and standard deviation 1. | ||
| + | |||
| + | Each of these random number generators has a matrix version, as well. E.g. | ||
| + | * **rand(m,n)**: an m x n matrix of random floating-point numbers between 0 and 1. | ||
| + | * **randi(m,n,max)**: an m x n matrix of random integers between 1 and max. | ||
| + | * **randn(m,n)**: an m x n matrix of a random numbers in a Gaussian distribution with mean 0 and standard deviation 1. | ||
| + | |||
| ==== if-else statements ==== | ==== if-else statements ==== | ||
| Line 121: | Line 133: | ||
| <code matlab> | <code matlab> | ||
| - | x = randn(); | ||
| x = randn(); | x = randn(); | ||
| if x < 0 | if x < 0 | ||
| Line 131: | Line 142: | ||
| end | end | ||
| </code> | </code> | ||
| + | |||
| + | ---- | ||
| + | ===== Lab material ==== | ||
| + | |||
| + | You should have a good grasp on the mathematics and Matlab programming of the lab material. For example, | ||
| + | |||
| + | ---- | ||
| + | ==== log-linear relations ==== | ||
| + | |||
| + | You should know how to infer a functional relation $y=f(x)$ given a logarithmic or linear plot | ||
| + | , and which of **plot**, **semilogx**, **semilogy**, and **loglog** is best for a given relation $y=f(x)$. | ||
| + | |||
| + | ---- | ||
| + | ==== writing functions ===== | ||
| + | |||
| + | You should know how to write Matlab functions that do basic computations, like matrix-vector multiplication. | ||
| + | |||
| + | ---- | ||
| + | ==== hamster dynamics / Google Page Rank ==== | ||
| + | |||
| + | Given a graph of nodes and one-way links between them, you should be able to write a system of equations that governs random walks through the network of links, and then write Matlab code that would calculate the steady-state distribution. | ||
| + | |||
| + | ---- | ||
| + | ==== nonlinear equations and Newton's method ==== | ||
| + | |||
| + | You should know the mathematics behind Newton's method for solving nonlinear equations, how to code it in Matlab, and how to use Matlab's built-in solver **fsolve** to solve nonlinear equations. | ||
| + | |||
| + | ---- | ||
| + | ==== differential equations ==== | ||
| + | |||
| + | You should know now how to write an anonymous function for a system of first-order differential equations $d\vec{x}/dt = \vec{f}(t, \vec{x})$, and how to solve that system of equations numerically using Matlab's **ode45**. And given a quiver plot of a 2-d differential equation, you should be able to draw an approximate solution of the equation starting from a given initial condition, by tracing out a curve that is everywhere tangent to the arrows. | ||
| - | * scripts: how to write scripts to perform a given sequence of commands. | ||
| - | * hamster dynamics / Google Page Rank: how to translate a graph of nodes and links to a transition matrix and then calculate the steady-state distribution. | ||
gibson/teaching/spring-2016/math445/finaltopics.1463404318.txt.gz · Last modified: 2016/05/16 06:11 by gibson
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