Upcoming SlideShare
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Standard text messaging rates apply

Partial

727

Published on

partial differential equations

partial differential equations

Published in: Education, Technology
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total Views
727
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
31
0
Likes
0
Embeds 0
No embeds

No notes for slide
• MRCE, B.Tech ECE 1st year
• MRCE, B.Tech ECE 1st year
• Transcript

• 1. APPLICATION OF PARTIAL DIFFERENTIAL EQUATIONS
• Presented By:
• Rahul Sharma
• Ravinder
• Tamesh
• Tejaasvi Bhogra
MRCE, B.Tech ECE 1st year
• 2. INTRODUCTION
• These equations are usually classified according to their mathematical form.
• Differential equations involving two or more independent variables are called partial differential equations.
• These equations may have only boundary conditions, in which they are referred to as Boundary Value Problems (BVP) or steady-state equations.
MRCE, B.Tech ECE 1st year
• 3. CLASSIFICATION
• Wave Equation :
• 1-D Heat flow :
• 2-D Heat flow:
MRCE, B.Tech ECE 1st year
• 4. Methods of Separation Of Variables
• Assumption
• Dependent Variable is the product of 2 functions, each involving only one of the independent Variables.
• Outcome : 2 Ordinary Differential Equations are Formed.
MRCE, B.Tech ECE 1st year
• 5. Equation of Vibrating String OR 1D Wave Equation
• The boundary conditions to be satisfied by the Equation are :
• y=0 ,when x=0
• Y=0 , when x =1
• [ These should be satisfied by every value of ‘t’ ]
MRCE, B.Tech ECE 1st year
• 6. 1 Dimensional Heat Flow = K/= K/s ρ which is known as Diffusivity of the material of the bar . Where , S = specific Heat ρ = density of material & K = Conductivity. MRCE, B.Tech ECE 1st year
• 7. SOLUTION OF THE HEAT EQUATION MRCE, B.Tech ECE 1st year
• 8. 2 D Heat Flow
• Note 1 : in the steady state,u is independent of t,so that du/dt = 0
• d2u/dx2 + d2u/dy2 = 0
• Which is Laplace’s Equation in 2-D
MRCE, B.Tech ECE 1st year
• 9. 2-D Heat Flow
• (d2u/dx2 + d2u/dy2 +d2u/dz2 ) = du/dt
• In Steady state,it reduces to
• (d2u/dx2 + d2u/dy2 +d2u/dz2 ) = 0
• Which is Laplace’s Equation in 3-D
MRCE, B.Tech ECE 1st year
• 10. Solution Of Laplace’s Equation in 2D MRCE, B.Tech ECE 1st year
• 11. THANK YOU MRCE, B.Tech ECE 1st year