channelflow.org

====== Differences ====== This shows you the differences between two versions of the page.

--- gibson:teaching:spring-2016:math445:finaltopics [2016/05/13 10:16]
gibson
+++ gibson:teaching:spring-2016:math445:finaltopics [2016/05/16 06:45] (current)
gibson [Plotting]
@@ Line 1: / Line 1: @@
 ====== 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). Below is a broad overview but not exhaustive of topics that might be covered on the exam.
 ----
+===== Matlab syntax =====
 ====Vectors and matrices====
@@ Line 53: / Line 56: @@
 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 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 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 ====
@@ Line 115: / 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 ====
+You should know how to write simple ''if-else'' statements such as
+<code matlab>
+x = randn();
+if x < 0
+  fprintf('%d is negative\n', x)
+elseif x == 0
+  fprintf('%d is zero\n', x)
+else
+  fprintf('%d is positive\n', x)
+end
+</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.
-...to be continued...
-  * **fprintf**: how to do basic formatted output with **fprintf**.
-  * 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.

channelflow.org

User Tools

Site Tools

Page Tools