4.4: The method of undetermined
coefficientsSuperposition approach
Now we would like to solve the nonhomogeneous nth-order linear DE
of the form
an (x)y(n) + an1 (x)y(n1) + + a1 (x)y0 + a0 (x)y = g(x).
(13)
Its associated homogeneous equation is
an (x)y(n
MATH 2350: Ordinary Differential equations
Chapter 6: Series Solutions of Linear
Equations
Instructor: Prof. Mahboub Baccouch, Associate Professor
[email protected]
DSC 233, Department of Mathematics
University of Nebraska, Omaha
In this chapter, we i
4.3 Homogeneous Linear Equations with Constant
Coefficients
In section 4.1 we saw the importance of having linearly independent
solutions in order to obtain the general solution for a homogeneous
nth-order linear differential equation. In particular, we s
3.1 Linear Models
3.2 Nonlinear Models
3.3 Modeling with Systems of First-Order DEs
MATH 2350: Ordinary Differential equations
Chapter 3: Modeling with first-order differential
equations
Instructor: Prof. Mahboub Baccouch, Associate Professor
[email protected]
7.4 Operational Properties II
We will learn some other techniques and operational properties of the
Laplace transforms.
Derivatives of a Transform Recall the transform of the derivative
from section 7.2:
Lcfw_f 0 (t) = sLcfw_f (t) f (0).
Thus, if f (0) =
MATH 2350: Ordinary Differential equations
Chapter 4: Higher-order Differential Equations
Instructor: Prof. Mahboub Baccouch, Associate Professor
[email protected]
DSC 233, Department of Mathematics
University of Nebraska, Omaha
In this chapter, we wi
MATH 2350: Ordinary Differential equations
Chapter 7: The Laplace Transform method
Instructor: Prof. Mahboub Baccouch, Associate Professor
[email protected]
DSC 233, Department of Mathematics
University of Nebraska, Omaha
The Laplace Transform techniq
4.6: The method of variation of parameters
So far we used the method of undetermined coefficients to solve the
following nonhomogeneous linear equation with constant coefficients:
an y(n) + + a1 y0 + a0 y = g(x),
(18)
where all the coefficients ai s are c
4.7: Cauchy-Euler equation
In the previous sections, we only found explicit solutions of
higher-order linear differential equations with constant coefficients.
The method we used does not, in general, apply to linear equations
with variable coefficients.
4.2 Reduction of order method
We know from the previous section that the general solution of a
homogeneous linear 2nd-order DE
a2 (x)y00 + a1 (x)y0 + a0 (x)y = 0,
(7)
is a linear combination y = c1 y1 + c2 y2 , where y1 and y2 are two
linearly independent
7.3 Operational Properties
We would like to increase our ability to find Laplace transforms of
given functions easily. We dont always want to use the definition of
Lcfw_f (t) each time we wish to find the LT of a function f (t). We will
learn techniques t
Introduction
2.1 Slope field
2.2 Separable DEs
2.3 Linear DEs
2.4 Exact DEs
2.5 Substitutions
2.6 Eulers method
2.4 Exact Differential Equations
First-order DEs are occasionally written in differential form
M(x, y )dx + N(x, y )dy = 0.
(8)
Dividing (8) by
7.2 Inverse Transforms and Transforms of Derivatives
As we said, the Laplace transform will allow us to convert a
differential equation for x(t) into an algebraic equation X(s) which we
can easily solve. Once we solve the algebraic equation in the
frequen
Introduction
2.1 Slope field
2.2 Separable DEs
2.3 Linear DEs
2.4 Exact DEs
2.5 Substitutions
2.6 Eulers method
2.5 Solutions by Substitutions (Substitution Methods)
So far, we have learned how to solve three kinds of first-order
DEs: separable, linear, a
Introduction
2.1 Solution curves without a solution
2.2 Separable equations
2.3 Linear first-order equations
2.3 Linear first-order equations
Linear equations are important because they arise frequently in
engineering and physics. Also because there are s
4.9: Solving Systems of Linear DEs by Elimination
So far we have discussed methods for solving an ordinary differential
equation (ODE) that involves only one dependent variable and one
independent variable i.e., we have only solved single ODEs. However,
m
1.1 Definitions and Terminology
1.2 Initial-Value Problems
1.3 Differential Equations as Mathematical Models
1.3 Differential Equations as Mathematical Models
We will see that DEs can be used to describe many real-world
problems. A DE that describes a phy
Introduction
2.1 Slope field
2.2 Separable DEs
2.3 Linear DEs
2.4 Exact DEs
2.5 Substitutions
2.6 Eulers method
2.6 Eulers method
Eulers method is a basic numerical method for approximating
solutions to IVPs. We note that there is no simple formula or
pro
Math 2350 - Summary of the power series method about an ordinary point - M. Baccouch
Summary: The power series method for solving a DE about an ordinary point x0 consists of substituting
P
n
the power series y =
n=0 cn (x x0 ) into the DE and then attemp
4.10: Nonlinear Differential Equations
In this section we will study some nonlinear higher-order equations.
Reducible Second-Order Equations: A second-order DE has the
general form
F(x, y, y0 , y00 ) = 0.
(27)
If either the dependent variable y or the ind
MATHEMATICAL ETHICS: VALUES, VALENCES AND VIRTUE
Douglas Henrich
Iroquois Ridge High School, Ontario, Canada
[email protected]
ABSTRACT
In this paper I will review the themes of: gender differentiation and engagement in
mathematics, ethics and separated va
Boolean Networks
Dr. Dora Matache
Homework: #2
Chapter 2
Becky Brusky
Due: 2/20/2014
Pattern Formation Rule 22, with CA
Pattern Formation Random Parents
Pattern Formation Random Parents
Pattern Formation Random Parents
The patterns that have been seen in
Boolean Networks
CHAPTER 1:
BOOLEAN FUNCTIONS
& CELLULAR AUTOMATA
Presented by Becky Brusky, January 16, 2014
Networks
A network is a collection of nodes
interconnected by links
(communication paths, or inputs).
Networks can interconnect with other
networ
Practice Test 2
Integrate the following.
1.
14 x sin x dx
2.
( x 28 x ) e x dx
3.
6
sin3 3 x dx
0
4.
7 dx
6+ x 2
5.
1
0
dx
16x 2
6.
dx
x 25 x29
7.
Use a substitution first.
ln 3
t
e dt
49+e 2 t
0
8.
11
x12 dx
2
36
7
9.
15 e15 x dx
0
10. Evaluate th
Practice Exam 1 Math 1960
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x—axis.
1)y=x2+3.
GENERAL INFORMATION
Blackboard will be used in this course. A copy of the syllabus and general information
can be found under Syllabus. Skills and review problems for each test will be found
under Course Materials at the appropriate time. Extra credit opp