L11 - Fall 2003 Math 308/501502 1 Introduction 1.1...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Fall 2003 Math 308/501–502 1 Introduction 1.1 Background Mon, 01/Sep c 2003, Art Belmonte Summary When modeling applications, equating the rate at which a quantity changes (a derivative) with an application-specific way of formulating the rate of change leads to a differential equation (DE) ; i.e., an equation that contains some derivative(s) of an unknown function. Recall the concept of proportionality . With k a constant (often positive), we have the following mathematical relationships (among many). MATH ENGLISH y = kx y is proportional to x y = kx 2 y is proportional to the square of x y = kxz y is proportional to the product of x and z y = k / x 3 y is inversely proportional to the cube of x d P / dt = kP the rate of change of P is proportional to P Here are some terms used in the study of differential equations. independent variable : a variable in a DE upon which the unknown function depends; often t (time) or x (when the context is geometrical). dependent variable : a variable whose derivative appears in a DE; usually y , occasionally x or some other letter. coefficients : multipliers of the unknown function or its derivatives, either constant or depending on independent variable(s) only. ordinary differential equations (ODEs) : differential equations containing only ordinary derivatives.
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern