Homework 10.
Due Friday, Nov. 4
Distinct real roots
1. Find the general solution of the given system of equations. Classify the type and
stability of the critical point at (0, 0).
1
1
0
x =
x
4 2
2. Solve the initial value problem. You may use general sol
Homework 6.
Due Friday, Oct. 7
Unforced & Forced Vibrations
1. Solve the following initial value problem, and determine the natural frequency, natural
period, amplitude and phase angle of the solution:
u00 + 100u = 0, u(0) = 3, u0 (0) = 0.
2. Consider a m
Homework 7.
Due Friday, Oct. 14
Definition of the Laplace Transform
1. Find the Laplace transform of each of the given functions (without table):
(a) f (t) = cos bt
(b) f (t) = eat cos bt
2. Find the Laplace transform of each of the given functions:
(a) f
Homework 3
Due Friday, Sept. 16
Falling Objects
1. A ball with mass 0.15 kg is thrown upward with initial velocity 20 m/s from the roof
of a building 30 m high. Assume that the force of air resistance is v 2 /1325. Find the
maximum height above the ground
Homework 5.
Due Friday, Sep. 30
Homogeneous Equation with Constant Coefficients;
Complex Roots of the Characteristic Equation
1. Find the general solution of the given differential equation.
(i) y 00 2y 0 + 6y = 0
(ii) y 00 + 2y 0 + 10y = 0.
2. Find the s
Homework 9.
Due Friday, Oct. 28
Second order differential equations
with discontinuous force and impulse function
In problems 1, 2, and 3 solve the initial value problem:
1. y 00 + 2y 0 + 3y = sin t + (t 3); y(0) = y 0 (0) = 0
2. y 00 + 3y 0 + 2y = (t 5)
Homework 2.
Due Friday, Sept. 9
Method of Integrating Factors
In problems 1 and 2 find the general solution of the given differential equation, and use it to
determine how solutions behave at t +.
1. (1 + t2 )y 0 + 4ty = (1 + t2 )2 .
2. y 0 + y = 5 sin 2t
Homework 4.
Due Friday, September 23
Exact Equations
1. Determine whether each of the following equations is exact. If it is exact, find the
solution.
(i) (3x2 2xy + 2) + (6y 2 x2 + 3)y 0 = 0
(ii) (ex sin y 2y sin x) + (ex cos y + 2 cos x)y 0 = 0
2. Deter
Homework 8.
Due Friday, Oct. 21
Laplace Transform
1. Find the Laplace transform of e3t f (t), if F (s) = L cfw_f (t) =
1
.
s6 +2
2. Find L cfw_cos2 t.
Step Functions
3. Sketch the graph of the given function on the interval t 0.
(a) g(t) = u1 (t) + 2u3 (t
Homework 1.
Due Friday, Sept. 2
Some Basic Mathematical Models; Direction Fields
In each of Problems 1 through 4 draw a direction field for the given differential equations. Based on the direction
field, determine the behavior of y as t +. If this behavio
Chapter 5: Control Structure
Logical Data Type
There are two possible values for logical data: true or false.
These values can be produced by:
1. Relational operators;
2. Logical operators;
3. Two special functions true and false.
Can mix numerical and lo
Chapter 3: MATLAB Fundamentals
Variable Types
MATLAB is a loosely or weakly typed language
- No need to explicitly declare the types of the variables
MATLAB supports various types, the most often used are
> 3.84
64-bit double (default)
>a
16-bit char
Mo
Chapter 2: Linear Algebra
What is Linear Algebra
Linear algebra is the study of vectors and linear functions.
In broad terms, vectors are things you add, and linear functions are
functions of vectors that complete vector addition.
What is Vector: Vectors
Chapter 4: Plotting
Graphics
MATLAB provides a variety of techniques to display data
graphically.
Interactive tools enable you to manipulate graphs to achieve
results that reveal the most information about your data.
You can also edit and print graphs
Presentations of Graphical Data
1. A frequency table is a list of a set of values and how many times they occur in the
set of data. This type of table is useful for large sets of data that makes it simpler
to calculate things like mean, median, and mode.
Linear Report Assignment:
1.
Discuss the question: What types of relationships can be modeled by a linear
equation? Can you justify why they are linear?
So many things can be modeled using linear models, but in general, they must be things
that have a con
Chapter 1:
What is Statistics?
Statistics is a collection of procedures and principles for gathering data and analyzing
information to help people make decisions when faced with uncertainty.
When we have a question that needs answering, we use statistics