Models ODE initial problem
... MATLAB provides for the solution of ODE variety of methods (ode45, ode113, ode15s, ...) which can automatically adjust the integration step so as to achieve the required accuracy. Procedure is always the same, first define a function whose output is the vector of first derivatives for a given value ...
... MATLAB provides for the solution of ODE variety of methods (ode45, ode113, ode15s, ...) which can automatically adjust the integration step so as to achieve the required accuracy. Procedure is always the same, first define a function whose output is the vector of first derivatives for a given value ...
An Analysis of the Collatz Conjecture
... Using a bisection algorithm we numerically approximated solutions to f (f (x)) − x = 0. Clearly these values approximate two-cycles and onecycles. With this list we can analyze the behavior of the two cycles by differentiating f (f (x)). If |f (f (x0 ))0 | < 1 we say (x0 , f (x0 )) is an attractor. ...
... Using a bisection algorithm we numerically approximated solutions to f (f (x)) − x = 0. Clearly these values approximate two-cycles and onecycles. With this list we can analyze the behavior of the two cycles by differentiating f (f (x)). If |f (f (x0 ))0 | < 1 we say (x0 , f (x0 )) is an attractor. ...
1 Section 1.1: Vectors Definition: A Vector is a quantity that has both
... Applications to Physics and Engineering: A force is represented by a vector because it has both magnitude (measured in pounds or newtons) and direction. If several forces are acting on an object, the resultant force experienced by the object is the vector sum of the forces. EXAMPLE 5: Ben walks due ...
... Applications to Physics and Engineering: A force is represented by a vector because it has both magnitude (measured in pounds or newtons) and direction. If several forces are acting on an object, the resultant force experienced by the object is the vector sum of the forces. EXAMPLE 5: Ben walks due ...
LB 220 Homework 1 (due Monday, 01/14/13)
... correctness) and late homework (homework is due at the start of class, late homework is assessed a 20% penalty if submitted within the next 48 hours) Collaboration. I encourage you to discuss the homework problems with your classmates. However, each student must write and submit his or her own homew ...
... correctness) and late homework (homework is due at the start of class, late homework is assessed a 20% penalty if submitted within the next 48 hours) Collaboration. I encourage you to discuss the homework problems with your classmates. However, each student must write and submit his or her own homew ...
Dynamical system
In mathematics, a dynamical system is a set of relationships among two or more measurable quantities, in which a fixed rule describes how the quantities evolve over time in response to their own values. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake.At any given time a dynamical system has a state given by a set of real numbers (a vector) that can be represented by a point in an appropriate state space (a geometrical manifold). The evolution rule of the dynamical system is a function that describes what future states follow from the current state. Often the function is deterministic; in other words, for a given time interval only one future state follows from the current state; however, some systems are stochastic, in that random events also affect the evolution of the state variables.