In pure mathematics, differential equations are studied from several different perspectives, mostly concerned with their solutions—the set of functions that satisfy the equation.

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Only the simplest differential equations are solvable by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form. Differential equations can be divided into several types.

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Apart from describing the properties of the equation itself, these classes of differential equations can help inform the choice of approach to a solution. The constant r will change depending on the species.

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Malthus used this law to predict how a species would grow over time. More complicated differential equations can be used to model the relationship between predators and prey.

## Engineering Differential Equations: Theory and Applications, Springer 2010

For example, as predators increase then prey decrease as more get eaten. But then the predators will have less to eat and start to die out, which allows more prey to survive.

The interactions between the two populations are connected by differential equations. We also learn how to find solutions that obey prescribed boundary conditions.

Not all DEs can be solved in terms of known functions such as polynomials, exponentials and the like. A major aim of this course is to teach you how to get information about the solution in these cases using power series methods and Frobenius method.

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## Differential Equations: Theory and Applications

A second major aim is to learn how to find solutions to boundary value problems using Sturm-Liouville methods and Fourier series methods. Skip to main content. This course was previously MATH a 3uoc course which is no longer offered.