วีดีโอ

21MAT11 : Solve 𝟑𝟐 𝝏𝒖/𝝏𝒕=(𝝏^𝟐 𝒖)/〖𝝏𝒙〗^𝟐 (𝟎, 𝟏) given that h=0.25, upto t=5 𝒖=(𝟎,𝒕)=𝟎=𝒖(𝟏,𝒕), 𝒖=(𝒙,𝟎). #MathEConnect #Shafiqahmedyellur

21MAT41 : Solve 𝝏𝒖/𝝏𝒕=(𝝏^𝟐 𝒖)/〖𝝏𝒙〗^𝟐 (𝟎, 𝟏 at t=0.002 𝒖=(𝟎,𝒕)=𝟎=𝒖(𝟏,𝒕), 𝒖(𝒙,𝟎)={(𝟐𝒙 (𝟎, 𝟎.𝟓) 𝟎@𝟐(𝟏−𝒙) (𝟎.𝟓, 𝟏) #MathEConnec #Shafiqahmedyellur

21MAT31 : Find the numerical solution of the parabolic equation (𝝏^𝟐 𝒖)/𝝏𝒙^𝟐 =𝟐 𝝏𝒖/𝝏𝒕 when 𝒖=(𝟎,𝒕)=𝟎=𝒖(𝟒,𝒕), 𝒖(𝒙,𝟎)=𝒙(𝟒−𝒙) by taking h=1, upto t=4 steps. #MathEConnect #Shafiqahmedyellur

21MAT31 : Numerical Solution of the one dimensional Heat equation & working procedure #MathEConnect #Shafiqahmedyellur

21MAT11 : Show that: 𝒊)𝑷_𝟐(𝒄𝒐𝒔𝜽)=1/4 (𝟏 𝟑𝒄𝒐𝒔𝜽) 𝒊𝒊) 𝑷_𝟑 (𝒄𝒐𝒔𝜽)=𝟏/� (𝟑𝒄𝒐𝒔𝜽 𝟓𝒄𝒐𝒔𝟑𝜽) #MathEConnect #Shafiqahmedyellur

21MAT41 : Express 𝒇(𝒙)=𝒙^𝟒−𝟑𝒙^𝟑−𝒙^𝟐 𝟓𝒙 in terms of Legendre polynomial. #MathEConnect #Shafiqahmedyellur

21MAT41 : Express 𝟐𝒙^𝟑−𝒙^𝟐−𝟑𝒙 𝟐 in terms of Legendre polynomial. #MathEConnect #Shafiqahmedyellur

21MAT41 : If 𝒙^𝟑 𝟐𝒙^𝟐−𝒙 𝟏=𝒂𝑷_𝟎 (𝒙) 𝐛_𝑷 𝟏( 𝒙) c𝑷 _𝟐 (𝒙) d𝑷_𝟑 (𝒙) .Find the value of a, b, c, d. #MathEConnect #Shafiqahmedyellur

21MAT41 : Express 𝒙^𝟑 𝟐𝒙^𝟐−𝟒𝒙 𝟓 in terms of Legendre polynomial #MathEConnect #Shafiqahmedyellur

21MAT41 : Rodrigues Formula & Results. #MathEConnect #Shafiqahmedyellur

21MAT41 : Series Solution Of Legendre’s Differential Equation.. #MathEConnect #Shafiqahmedyellur

21MAT41 : Orthogonality of Bessel s Functions #MathEConnect #Shafiqahmedyellur

Prove that : 𝑱((−𝟏)⁄𝟐) (𝒙)=√(𝟐/𝝅𝒙) 𝒄𝒐𝒔𝒙.

Prove that : 𝑱(𝟏⁄𝟐) (𝒙)=√(𝟐/𝝅𝒙) 𝒔𝒊𝒏𝒙.

Bessel's Functions: Series solution of Bessel's Differential Equation Leading to Bessel's Function.

Solve the wave equation (𝝏^𝟐 𝒖)/〖𝝏𝒙〗^𝟐 =(𝝏^𝟐 𝒖)/〖𝝏𝒕〗^𝟐 𝒖(𝒙,𝟎)=𝒔𝒊𝒏𝝅𝒙 (0,1), h=0.2, k=0.2 at 𝒕=𝟏.

Solve the wave equation 25 (𝝏^𝟐 𝒖)/𝝏𝒙^𝟐 =(𝝏^𝟐 𝒖)/𝝏𝒕^𝟐 𝒖(𝒙,𝟎)={(𝟐𝟎𝒙 𝟎≤𝒙≤𝟏, 𝟓(𝟓−𝒙) 𝟏≤𝒙≤𝟓) h=1, 𝟎≤𝒕≤𝟏.

Solve the Wave equation (𝝏^𝟐 𝒖)/(𝝏𝒙^𝟐) =𝟎.𝟎𝟔𝟓 (𝝏^𝟐 𝒖)/𝝏𝒕^𝟐 , 𝒖(𝒙,𝟎)=𝒙^𝟐 (𝒙−𝟓), h=1, k=0.5 ,4 steps.

Solve the wave equation (𝝏^𝟐 𝒖)/〖𝝏𝒕〗^𝟐 =𝟒 (𝝏^𝟐 𝒖)/〖𝝏𝒙〗^𝟐 𝒖(𝒙,𝟎)=𝒙(𝟒−𝒙) , h=1, k=0.5 upto 4 steps.

Working procedure for one dimensional wave equation

21MAT31: Numerical solution of the one dimensional wave equation.

21MAT31:Numerical Method PDE, Classification of PDE of second order & Finite difference approximate.

# Partial Derivatives || # Definition || #Symbols

#Evaluate || lim_𝒙→𝟎⁡(𝒔𝒊𝒏𝒙𝒙^𝟏⁄𝒙^𝟐 ) || 21MAT11 || Module : 2 || Differential Calculus ||BMATE101

Evaluate || lim_𝒙→𝟎⁡(𝒕𝒂𝒏𝒙𝒙^𝟏⁄𝒙 ) || 21MAT11 || Module : 2 || Differential Calculus ||

Evaluate || lim┬(𝒙→𝟎)⁡[((𝒂^𝒙 𝒃^𝒙 𝒄^𝒙 𝒅^𝒙 ))/𝟒]^(𝟏⁄𝒙) || 18MAT11 || Differential Calculus

Evaluate || lim_𝑥→𝜋/2⁡(𝒔𝒊𝒏𝒙^𝒕𝒂𝒏𝒙 )|| 18MAT11 || Differential Calculus

Evaluate || lim┬(𝒙→𝟎)⁡ ([𝒄𝒐𝒔𝒙]^(𝟏⁄𝒙^𝟐 )) || Differential Calculus || #Math E Connect

Evaluate || lim_(𝒙→𝟏)⁡(𝒙^(𝟏⁄(𝟏−𝒙)) )|| Differential Calculus || #Math E Connect||