Download - Cauchy riemann equations
GROUP #04
M.Naveed 12-EL-16
H.M Sajid Iqbal 12-EL-29
M.Ishtiaq zahoor 12-EL-64
Amir khan 12-EL-25
Waqar Siddique 12-EL-20
Zeshan Aadil 12-EL-69
Group leaderM.Naveed
TOPICWhat is Cauchy Riemann
equation ?
Application of Cauchy Riemann equation in
engineering
Application of Cauchy Riemann equation in real
life
HISTORY
Cauchy Riemann equation named after Augustin Cauchy and Bernhard
Riemann
it is discovered in 1851 during work on the theory of
the functions
IMPORTANT FEATURESCauchy Riemann equation also known as
D”Alembret Euler condition
It is use to check differentiability of a complex function
It is used for verification of the analicity of the given function
It is used to find the harmonic conjugate of a function
CAUCHY RIEMANN EQUATION
• Definition
if f(z)=u(x,y)+i(x,y) and x=rcos(theta) ; y=rsin(theta)
Therefore u and v are the function of r and theta.
Then Cauchy Riemann equation Cartesian co-ordinate is given as
1. du/dx =dv/dx ; 2. dv/dx= -du/dx
in polar form
1. du/dr=1/r(dv/d*) 2. dv/dr= -1/r(du/d*)
ANALYCITY OF A FUNCTION
DRAMATIC DISCOVERY OF CAUCHY RIEMANN EQUATION
• Aungestin Cauchy was a civil engineer and mathmation also..
• During his survey for the dam he got this idea ……..
APPLICATION IN ENGINEERING• Triangular grid generation
According to the research paper of Hiroaki nishkiwa on computational fluid dynamics ……. Department of aerospace engineering university of Michigan(30th march 1999)
TRIANGULAR GRID GENERATION
TENTION OF SUBSTANCES IN SPACE
OTHER APPLICATION
• Following are the other application driven with help of Cauchy Riemann equation are……………….
• Calculation of fluid intensity at a point in the fluid
• For the verification of Maxwell equation
• In divergence theorem to give the rate of change of a function
APPLICATION IN REAL LIFE
• To move point a function from Cartesian to polar co-ordinate by D.Alembret Euler condition
OTHER APPLICATION
• To prove function analytic
• To find harmonic conjugate of a function
Thank you
Any question