RainmanTime
Timekeeper
The mathematics of vector and tensor integro-differential equations are extremely powerful in helping us model the physical reality of our universe.
Here is just a partial list of the kinds of things we can model with integro-diff EQs:
<font color="blue">
Acceleration of free-falling objects
Vertical displacement of a weight attached to a string
Pendulum of a weight in a vertical plane
Population growth
Spread of disease
Newton's law of cooling
Compound interest
Shape of a hanging wire
Motion of coupled weights
Velocity of a falling weight
Water flowing through an orifice
The Tractrix
Motion of projectiles
Drug infusion into bloodstream
Reflection of light
Distance a rocket travels
Motion of a weight in an inclined plane
Orthogonal trajectories
Growth & decay
Carbon dating
Thermal cooling
General circuits
Chemical mixtures
Population growth & logistic curves
Chemical reactions
Laws of radiation
Biologiocal imbalance of predator and prey
Pursuit curves
Two-body problem
Least TIME problem
Law of Malthus
Simple harmonic motion
Damped motion
Forced motion
Resonant motion
Series electrical systems
Series torsional systems
Airplane wings
Current in electrical circuits
Coupled weights and springs
General Networks
Mixtures
Heat Equations
Temperature in a mass rod
Insulated boundaries
Quantum wave equation
Vibrating strings
Laplace's equation
Temperature in a mass plate [/COLOR]
<font color="red"> ...and so many other physical applications... [/COLOR]
RMT
Here is just a partial list of the kinds of things we can model with integro-diff EQs:
<font color="blue">
Acceleration of free-falling objects
Vertical displacement of a weight attached to a string
Pendulum of a weight in a vertical plane
Population growth
Spread of disease
Newton's law of cooling
Compound interest
Shape of a hanging wire
Motion of coupled weights
Velocity of a falling weight
Water flowing through an orifice
The Tractrix
Motion of projectiles
Drug infusion into bloodstream
Reflection of light
Distance a rocket travels
Motion of a weight in an inclined plane
Orthogonal trajectories
Growth & decay
Carbon dating
Thermal cooling
General circuits
Chemical mixtures
Population growth & logistic curves
Chemical reactions
Laws of radiation
Biologiocal imbalance of predator and prey
Pursuit curves
Two-body problem
Least TIME problem
Law of Malthus
Simple harmonic motion
Damped motion
Forced motion
Resonant motion
Series electrical systems
Series torsional systems
Airplane wings
Current in electrical circuits
Coupled weights and springs
General Networks
Mixtures
Heat Equations
Temperature in a mass rod
Insulated boundaries
Quantum wave equation
Vibrating strings
Laplace's equation
Temperature in a mass plate [/COLOR]
<font color="red"> ...and so many other physical applications... [/COLOR]
RMT
