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