MATH 238: Differential Equations

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Class Program

Mathematics

Credits

Clinical Hours None

Weekly Contact Hours

Course ID

091766

Meets Degree Requirements For

Natural Science,

Quantitative Skills

Description

Modeling with and solving of first- and higher-order ordinary differential equations, systems of linear equations, Laplace Transforms and series solutions of linear differential equations. Methods include numerical, qualitative and analytic approaches. The course will include modeling applications in engineering, chemistry and population studies.

Grading Basis

Graded

Prerequisites

MATH& 152 or Instructor Permission

Course Learning Outcomes

Set up and solve ordinary differential equations including but not limited to:
<ul>
<li>Linear</li>
<li>Exact</li>
<li>Separable</li>
<li>Bernoulli</li>
<li>Higher-order constant coefficient linear equations both homogeneous and non-homogeneous</li>
<li>Cauchy - Euler equations</li>
<li>Systems of linear differential equations</li>
</ul>

Use a variety of problem-solving techniques including:
<ul>
<li>finding a second solution from a first</li>
<li>separation of variables</li>
<li>reduction of order</li>
<li>undetermined coefficients</li>
<li>variation of parameters</li>
<li>Laplace Transforms</li>
<li>Implement power series solution methods especially Taylor series</li>
<li>Use analytical, numerical, and qualitative solution techniques</li>
<li>Solve Initial and Boundary value problems for particular solutions</li>
</ul>

Express an application as a math model and solve it using one of the techniques mentioned above. Check their results for reasonableness for the model.

Core Topics

First order differential equations including existence and uniqueness theorem and differential equations of the following types: separable, linear, exact, homogeneous and equations reducible to first order.
Higher-order linear differential equations including the topics of linear independence and the Wronskian, existence and uniqueness of solutions, homogeneous and non-homogeneous DE with constant coefficients, Cauchy-Euler’s DE.
Linear systems of differential equations including methods of elimination and matrix methods.
Method of Laplace transforms to solve DE.
Series Solutions of second –order linear equations
Boundary value problems and eigenvalues and eigenfunctions
Numerical solution techniques including Euler’s, Taylor-series methods.
Stability analysis and phase plane solution curves.
Applications for each of the above types of equations which require creating the model and solving the resulting equation or system.