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Applications
Of Differential
Equations in Data
Science
Introduction
Modeling Complex Systems is crucial
for understanding many real-world
phenomena in science and
engineering. Differential Equations
play a key role in modeling such
systems.This presentation will
describe the importance of
differential equations in data science.
What are Differential Equations?
A differential equation is an equation
that relates a function to its
derivatives.They are used to model
many physical and biological systems.
There are two types:ordinary
differential equations and partial
differential equations.
Applications of Differential Equations
Differential equations are used to model a wide
variety of systems,including population growth,
heat transfer, fluid dynamics, and chemical
reactions. Solving these equations allows us to
make predictions and understand the
underlying mechanisms of these systems.
Numerical Methods for Solving Differential
Equations
Exact solutions to differential equations are often
difficult or impossible to find. Instead, numerical
methods are used to approximate solutions.
These methods include Euler's method, Runge-
Kutta methods, and finite difference methods.
E amples of Differential Equation
Models
Differential equations can be used to
model a wide range of phenomena,
from the spread of infectious diseases
to the behavior of financial markets.
Examples include the SIR model,
which models the spread of disease,
and the Black-Scholes model, which
models stock prices.
Conclusion
Differential equations are a powerful tool for modeling
complex systems. They allow us to make predictions and
understand the underlying mechanisms of these systems.
While exact solutions are often difficult or impossible to find,
numerical methods provide a way to approximate solutions.
Differential equations will continue to play a key role in data
science and other fields.
OD&VC.pptx

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OD&VC.pptx

  • 2. Introduction Modeling Complex Systems is crucial for understanding many real-world phenomena in science and engineering. Differential Equations play a key role in modeling such systems.This presentation will describe the importance of differential equations in data science.
  • 3. What are Differential Equations? A differential equation is an equation that relates a function to its derivatives.They are used to model many physical and biological systems. There are two types:ordinary differential equations and partial differential equations.
  • 4. Applications of Differential Equations Differential equations are used to model a wide variety of systems,including population growth, heat transfer, fluid dynamics, and chemical reactions. Solving these equations allows us to make predictions and understand the underlying mechanisms of these systems.
  • 5. Numerical Methods for Solving Differential Equations Exact solutions to differential equations are often difficult or impossible to find. Instead, numerical methods are used to approximate solutions. These methods include Euler's method, Runge- Kutta methods, and finite difference methods.
  • 6. E amples of Differential Equation Models Differential equations can be used to model a wide range of phenomena, from the spread of infectious diseases to the behavior of financial markets. Examples include the SIR model, which models the spread of disease, and the Black-Scholes model, which models stock prices.
  • 7. Conclusion Differential equations are a powerful tool for modeling complex systems. They allow us to make predictions and understand the underlying mechanisms of these systems. While exact solutions are often difficult or impossible to find, numerical methods provide a way to approximate solutions. Differential equations will continue to play a key role in data science and other fields.