MATH 2214 Syllabus Spring 2017
Textbook: Elementary Differential Equations with Boundary Value Problems (2nd Edition). Kohler and
Johnson.
Note: It is recommended that graphical and numerical problems
6.1 Introduction to Nonlinear Systems
We saw in Chapter 4 that some physical systems require several variables to
describe their state. Consequently, the differential equations that model the
behavior
4.9 Numerical Methods for Systems of Linear
Differential Equations
In Section 2.10 we introduced Eulers method. It was a numerical algorithm
for approximating solutions of the equations of the followi
2.2 First Order Linear Differential Equations
Solving the Linear Homogeneous Equation
We start with rewriting the equation y 0 + p(t)y = 0 in the form:
Example 1: Find a solution of the equation y 0 +
4.3 Homogeneous Linear Systems
We will develop methods for solving linear systems by going through the same
steps as we did before. First, we investigate the properties of homogeneous
systems. Then, w
2.3 Introduction to Mathematical Models
Now that we know how to solve linear ODEs, we can solve some application
problems!
Modeling Mixing Problems
Assume a salt solution enters a tank (which already
2.9 Applications to Mechanics
Newtons Second Law:
What if we drop a ball? Assume there is no air resistance and the only force
is the weight of the object.
What if we have air resistance?
1
Case 1: Dr
3.8 The Method of Undetermined Coefficients
We can summarize the process of solving the Initial Value Problem
y 00 + p(t)y 0 + q(t)y = g(t), y(t0 ) = y0 , y 0 (t0 ) = y00
1. Find the general solution:
3.2 The General Solution of Homogeneous Equations
Some Review of Linear Algebra
Definition
The set S = cfw_v1 , v2 , . . . vn is a Linearly Independent Set if
?
Theorem
The Following Are Equivalent:
3.5 Complex Roots
In this case the roots of characteristic polynomials are
For convenience we denote
and our solutions become:
We need to clarify the mathematical meaning of these two expressions. How
4.8 Nonhomogeneous Linear Systems
We now address the problem of finding the general solution to the nonhomogeneous
first order system
Notice a couple of changes:
1) There is a term g(t) that makes the
1.3 Direction Fields
Direction fields will help us to understand the differential equations of the
form:
The direction fields provide the insight into the qualitative behavior of solutions of a differ
6.2 Equilibrium Solutions and Direction Fields
Nonlinear first order systems are quite challenging to solve. Fortunately, for
most of the situations, there is no need for an accurate solution. For exa
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6.4 and 6.6 Stability and TwoDimensional Linear
Systems
Differential equations are at the core of many mathematical models of different physical processes. The solution to the differential equation r
Name:
MATH 2214 Exam 1
Instructions: Answer each question to the best of your ability. In order to receive full
credit for a question, you must show your work, use only methods learned in this class,
4.10 The Exponential Matrix and Diagonalization
In Section 2.2 we learned that the solution to the scalar first order initial
value problem y 0 = ay, y(0) = y0 is
For first order systems, if A is a co
Name:
MATH 2214 Exam 2
Instructions: Answer each question to the best of your ability. In order to receive full
credit for a question, you must show your work, use only methods learned in this class,