Math 272  Assignment #5
Week 5  Secant Method, fzero, Interpolation
1. Use the Secant method to nd the stated number of solutions to the following equations.
Report your starting values
Report the solutions to 5 signicant digits.
You must be able to
Math 272  Assignment #2
Week 2  Linear Systems, Truss and Thermo Applications
Note: you will not be asked to solve a complete problem like #4#8 on the test. However, you will be asked to solve
part of such a problem. e.g. you might be given the matrix
Math 272  Assignment #3
Week 3  Graphing, Sparse Matrices, and System Solving
1. Plotting TwoVariable Functions
We can use the meshgrid command not just for plots of matrices we build ourselves, but also to draw graphs of
twovariable functions.
Have M
Math 272  Assignment #6
Week 6  Function Fitting
1. For each of the datasets DatasetQ1A.xlsx through to DatasetQ1D.xlsx,
download the data le on to the local computer,
load its data into MATLAB using xlsread,
plot the two columns of the data as a scatte
Math 272  Assignment #7
Week 7  Animation, Intro to Integration
1. Animation and Movies
The position of a point moving counterclockwise along a unit circle follows the coordinates given by (x, y) = (cos(t), sin(t).
Note: Dont forget that the pressing <
WEEK #10, Lecture 1: Introduction To Optimization
Optimization Intro
Many design problems and applications involve the search for the best parameters
to achieve a goal. Examples include nding
2
In all these cases, we assume that
there is a single variabl
Math 272  Assignment #8
Week 8  ODE Solving
1. Use ode45 to generate a graph of the solution to the following DEs, over the specied interval, given the initial condition.
dy
= t2 + y 2 , y(0) = 0, and 0 t 1.
dt
dy
= sin(t) + cos(y), y(0) = 0, and 0 t 10
Math 272  Assignment #4
Week 4  NonLinear Solving, MATLAB Functions
Writing MATLAB functions
1. Write the function f (x) = x3 + sin(x) as
an anonymous function (using the @ symbol)
a full MATLAB function (in a separate .m le)
f = @(x) x.^3 + sin(x)

Math 272  Assignment #10
Assignment #10  Optimization
1. A missile has a guidance device which is sensitive to both temperature, t o C, and humidity, h. The range in km over
which the missile can be controlled is given by
Range R(h, t) = 27, 800 5t2 4ht
WEEK #10, Lecture 2: Constrained Optimization
Optimization Refresher
Many design problems and applications involve the search for the best parameters
to achieve a goal. Examples include nding:
The choice of track supports that minimizes the time for the
WEEK #7, Lecture 3: Adaptive Methods, Integration from Data
We have seen the family of NewtonCotes Methods for estimating denite
integrals.
order 0
order 1
order 2
There is no question that Simpsons rule was the most ecient of these methods. We also d
WEEK #7, Lecture 1: Introduction to Numerical Integration
Heat Transfer
Consider the cooling n shown below:
We x the temperature at the base, and ask the question
How quickly is heat radiated out of n?
2
What factors aect the rate of heat transfer out of
.
WEEK #9, Lecture 3: Modern ODE Solvers; Events
Last Class
We saw how the simple calculus approximation
dy
t
y
dt
could be used to update/simulate y over time, based on a dierential equation. All
we needed was:
dy
A way to calculate
, a dierential equa
Math 272  Assignment #11
Week 11  Optimization
1. Consider a set of 5 points joined together by a collection of springs. The locations of the ve points can be dened by
two 5element vectors x and y. The function systemSpringEnergy(x, y) will compute the
Math 272  Assignment #9
Week 9  Further ODE Solving
As part of this assignment, you should be able to reproduce the Eulers and Heuns method for numerical solving ODEs.
dy
Your methods should be able to handle both singlevariable DEs
as well as systems
WEEK #8, Lectures 13: Numerical DE Solving
ODE Solving
One of the key simulation step in the roller coaster project will be using net forces
to predict motion.
Input: forces
Leads to: dierential equation
The solution to DE is .
2
Heating and Cooling
Le
WEEK #9, Lecture 1: Fundamentals of Numerical DE Solving
ODEs Without Simple Solutions
We saw last week how we could get numerical/approximate solutions to dierential
equations. The reason we use numerical methods is because the ODEs for many
practical ap
Math 272  Assignment #1
MATLAB
Solutions
1. Create a vector with the values 3, 6, 9, . . ., 300, and store it in the vector v.
v = 3:3:300
2. Create a vector with the values 22 , 42 , 62 , . . . , 102 , and store it in the vector v.
Three (of many) optio