Differential equations have a variety of applications and uses in science, engineering, and everyday life. They were first developed with the invention of calculus in the 17th century and have since been used to model phenomena in fields like physics, chemistry, biology, economics, and more. Differential equations can model systems involving rates of change, like population growth, chemical reactions, motion, networking patterns, and other dynamic systems and processes.

2. DIFFERENTIAL EQUATION IN CSE & REAL LIFE

3. Presented by:
➤ Md.Noman Hasan
ID:182-15-2172.

4. History of the Differential Equation :
• Period of the invention.
->differential equations first came into existence with the invention
of calculus by Newton and Leibniz.
• Who developed the methods.
->The Euler–Lagrange equation was developed in the 1750s by Euler.

5. • Who invented the idea.
->Jacob Bernoulli proposed the Bernoulli differential equation in 1695.

6. Many types of DE:
• Ordinary differential equations.
• Partial differential equations.
• Non-linear differential equations.
• Complex differential equation.
• Exact differential equation .
• Homogeneous/Inhomogeneous.

8. • Fluid mechanics.
• Statics/dynamics.
• Mass transfer.
• Signals and systems.

11. Biologycal term:
 Verhulst equation – biological population growth
 von Bertalanffy model – biological individual growth
 Replicator dynamics – found in theoretical biology
 Hodgkin–Huxley model – neural action potentials

13. Applications of DE
• Software.
->computer hardware.
• Logic programming.
->To create a logic we also use DE.

14. • Making Game FEATURES .
->Differential equation is used to model the velocity of a character.
• Networking
->To understand a outcome of a edge creation model like preferential
attachment which says that nodes with probability proportional to
their existing degrees.

16. • Artificial Intelligence.
->MR images demonstrate, thin-plate spline , Images generated using
sensitivity encoding.
• In THEORIES & Explanations
->Exponential Decay The rate of decay of a radioactive substance at a
time t is proportional to the mass x(t) of the substance left at that time.

17. Differential Equations in our every day life!!
In medicine.
->for modelling cancer growth or the spread of disease.
In chemistry.
->for modelling chemical reactions and to computer radioactive half
life.

19. In economics.
-> to find optimum investment strategies.
In physics.
-> to describe the motion of waves, pendulums or chaotic systems.