From the course: Complete Guide to Differential Equations Foundations for Data Science

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Sturm-Liouville boundary value problems

Sturm-Liouville boundary value problems

From the course: Complete Guide to Differential Equations Foundations for Data Science

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Sturm-Liouville boundary value problems

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- [Instructor] Let's explore a particular type of boundary value problem you'll frequently come across when working with boundary value problems. These are called the Sturm-Liouville boundary value problems. Let's explore what these are. Sturm-Liouville boundary value problems are named after the two French mathematicians, Jacques-Charles-Francois Sturm and Joseph Liouville. These problems are a class of eigenvalue problems for second-order, linear differential equations. They often provide the framework for solving partial differential equations using a technique called separation of variables. This technique will be explored more in the next chapter when you work with partial differential equations. Sturm-Liouville boundary value problems are defined with the following equation where you have d/dx multiplied by p of x multiplied by dy/dx plus q of x multiplied by y plus lambda multiplied by w of x multiplied by y equals zero. In this equation, you have your given functions, p of x…

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