and a term limiting growth due to crowding The differential equation is dP dt

And a term limiting growth due to crowding the

This preview shows page 7 - 9 out of 12 pages.

and a term limiting growth due to crowding The differential equation is dP dt = rP 1 - P M P is the population, r is the Malthusian rate of growth, and M is the carrying capacity of the population This is a first order , nonlinear , homogeneous differential equation We solve this problem later in the semester Joseph M. Mahaffy, h [email protected] i Lecture Notes – Introduction to Differential Equa — (28/47)
Image of page 7

Subscribe to view the full document.

The Class — Overview The Class... Introduction Applications of Differential Equations Checking Solutions and IVP Evaporation Example Nonautonomous Example Introduction to Maple Applications of Differential Equations 5 The van der Pol Oscillator: In electrical circuits, diodes show a rapid rise in current, leveling of the current, then a steep decline Biological applications include a similar approximation for nerve impulses The van der Pol Oscillator satisfies the differential equation v 00 + a ( v 2 - 1) v 0 + v = b v is the voltage of the system, and a and b are constants This is a second order , nonlinear , nonhomogeneous differential equation This problem does not have an easily expressible solution, but shows interesting oscillations Joseph M. Mahaffy, h [email protected] i Lecture Notes – Introduction to Differential Equations — (29/47) The Class — Overview The Class... Introduction Applications of Differential Equations Checking Solutions and IVP Evaporation Example Nonautonomous Example Introduction to Maple Applications of Differential Equations 6 Lotka-Volterra – Predator and Prey Model: Model for studying the dynamics of predator and prey interacting populations Model for the population dynamics when one predator species and one prey species are tightly interconnected in an ecosystem System of differential equations x 0 = a x - b xy y 0 = - c y + d xy x is the prey species, and y is the predator species This is a system of first order , nonlinear , homogeneous differential equations No explicit solution, but we’ll study its behavior Joseph M. Mahaffy, h [email protected] i Lecture Notes – Introduction to Differential Equa — (30/47) The Class — Overview The Class... Introduction Applications of Differential Equations Checking Solutions and IVP Evaporation Example Nonautonomous Example Introduction to Maple Applications of Differential Equations 7 Forced Spring-Mass Problem with Damping: An extension of the spring-mass problem that includes viscous-damping caused by resistance to the motion and an external forcing function that is applied to the mass The model is given by my 00 + cy 0 + ky = F ( t ) y is the position of the mass, m is the mass of the object, c is the damping coefficient, k is the spring constant, F ( t ) is an externally applied force This is a second order , linear , nonhomogeneous differential equation We’ll learn techniques for solving this Joseph M. Mahaffy, h [email protected] i Lecture Notes – Introduction to Differential Equations — (31/47) The Class — Overview The Class...
Image of page 8
Image of page 9
  • Fall '08
  • staff

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

Ask Expert Tutors You can ask You can ask ( soon) You can ask (will expire )
Answers in as fast as 15 minutes