MA2250 Section 2.1
Mathematical Models. Population Models. Logistic Model Using
First Order Dierential Equation
Claire Watson
September 13, 2016
1. Exponential Models
dP
Earlier in Chapter 1, the change in the population P (t) is described by
= kP , k >
MA2250 Section 2.2
Equilibrium Solutions
Claire Watson
September 18, 2016
1. Autonomous Equations
An autonomous equation is a first-order dierential equation in which the independent
variable does not appear explicitly.
It has the general form
dy
= y 0 =
MA2250 Section 1.3 Part I
Slope Fields and Solution Curves
Claire Watson
September 1, 2016
Sections 1.1 and 1.2 looked at the analytic behavior of the solutions.
In this section, the first topic investigates the qualitative and geometric behaviors of so
MA2250 Section 1.4
Separable Equations and Applications
Claire Watson
September 7, 2016
Direct integration was used in section 1.1 to obtain the general solution of a dierential equation.
Example:
1. Study of Solving First Order Dierential Equations
The f
MA2250 Section 2.3
Acceleration. Velocity Models
Claire Watson
September 20, 2016
In the investigation of problems modeled through first-order dierential equations, a model
was introduced in section 1.2 involving an object of mass m moving along a vertic
MA2250 Section 1.3 Part II
Existence and Uniqueness
Claire Watson
September 1, 2016
1. Introduction
So far, we have assumed that a solution existed. To find solutions of dierential equations
we may :
Use straight integration if possible.
If an antideriv
MA2250 Section 1.6
Claire Watson
September 11, 2016
Substitution Methods
Many applications involve dierential equations that can neither be solved using the method
of separation of variables nor the integrating factor method.
This section shows how subs
MA2250 Section 3.1
Linear Systems and Matrices
Claire Watson
September 25, 2016
1. Introduction
Until now, methods of solution were for single ordinary equations.
In practice, a system may require more than one dierential equation to describe it, and
th
MA2250 Section 1.2
Integrals as General and Particular Solutions
Claire Watson
August 31, 2016
1. First Order Equations
So far, a dierential equation
dy
= f (x), will give
dx
y=
as the general solution, if we integrate both sides.
The slopes depend only o
MA2250 Section 1.1
Dierential Equations and Mathematical Models
Claire Watson
August 29, 2016
Dierential equations are important: they occur in every discipline that deals with rates of
change.
Two main themes: modeling (deriving a dierential equation)
MA2250 Section 1.5
Integrating Factor Method
Claire Watson
September 9, 2016
The method of separation of variables implies that the derivative of a function can be expressed
as a product, or a ratio, of two functions, one in x and one in y. All separable
Chapters 1-3
Dot product=viwi+
Chapters 3-5
Schwarz Inequality=|vw|vw
Triangle Inequality=v+wv+w
C(A)
Linear Dependence (Singular)
Linear Independence (Invertible)
Elimination
Lij=mult/pivot
Matrix: place -lij in i,j in E
Upper Triangular (U)
Diags=pivots