Textbook Guide Mathematics: Carrying Capacity, Integrating Factor, Restoring Force

• School: UTSG
• Department: Mathematics
• Course: MAT133Y1
• Professor: all

Document Summary

Models of population growth: variables: t = time (the independent variable) P = the number of individuals in the population (the dependent variable: assumption: where k is the proportionality constant, any exponential function of the form is a solution, another model: A model for the motion of a spring: restoring force = -kx, by newton"s second law, this is an example of what is called a second-order differential equation. General differential equations: in general, a differential equation is an equation that contains an unknown function and one or more of its derivatives. The order of a differential equation is the order of the highest derivative that occurs in the equation: the problem of finding a solution of the differential equation that satisfies the initial condition is called an initial-value problem. Direction fields: the direction field allows us to visualize the general shape of the solution curves by indicating the direction in which the curves proceed at each point.