Differential equations

1. ASSIGNMENT TOPIC:
APPLICATIONS OF DIFFERENTIALEQUATIONS
DISCIPLINE :
BS (HONS)COMPUTERSCIENCES
SUBMITTED BY:
KHADIJA TAHIRA 043
SUBMITTED TO :
MA’AM RUBINA SHUAIB

2. Differential Equation
“Differential Equation is an equation involving derivatives
of a function or functions”
Applications of Differential Equations:
 Creating Softwares
 Constraint Logic Programming
 Creating Games, Aspects of Algorithms
 Mother Nature
 Bots
 Artificial Intelligence
 Networking
 In Theories and Explanations
Softwares
The use of differential equations to understand computer hardware
belongs to applied physics or electrical engineering.
Constraint Logic Programming
A constraint logic programming is a logic that contains constraints in
the bodyof clauses. It’s very necessitated for many terms of Civil Engineering, ME,
DE and Most importantly this includes Differential Equations.
Gaming Features
Differential equation is used to model the velocity of a character.
Differential equation is an essential tool for describing the nature of the physical
universe and naturally also an essential part of models for computer graphics and
vision.

3. Aspects of Algorithms
Machine learning it includes computervision. Also involves solving for
certain optimal conditions or iterating towards a solution with techniques like
gradient descent or expectation maximization.
Mother Nature
Differential equations is an essential tool for describing the nature of
the physical universe.
BOTs
PDEs (partial differential equations) , ODE (Ordinary differential
equations) like this helps to provide shape and interior and exterior designs of
machine.
Artificial Intelligence
MR images demonstrate, thin-plate spline(TPS),Images generated
using sensitivity encoding(SENSE),Gaussian Kernel smoothed (GKS).
Networking
To understand a outcome of a edge creation model like preferential
attachment which says that nodes with probability proportional to their existing
degrees.
In Theories and Explanations
Newton’s law of cooling
dθ /dt=-k(θ- θs)
where θ= θ (t)
θ= θo at t=0.
Exponential Decay
The rate of decay of a radioactive substance at a time t is
proportional to mass x(t) of the substance left at that time.

4. PhysicalLaws:
Gauss’s law in electrostatics, magnetism and gravity.
Continuity equations- In fluid dynamics, electromagnetism, quantum mechanics,
relativity theory.
If a temperature is kept constant, the velocity of chemical reaction is proportional
to the productof the concentration of the substancewhich is reacting.