10 тысяч подписчиков
523 видео
#27 || Problem on Solution of Lagrange’s linear PDE|| Solve: (𝒚^𝟐 𝒛)/𝒙 𝒑+𝒙𝒛𝒒=𝒚^𝟐|| 18MAT21|| #PDE||
#31|| Problem#3 || Construction of interpolation polynomial|| Newton’s general interpolation ||
#7 || Problem#3 | Form a PDE by eliminating the arbitrary function of the equation 𝒛=𝒇(𝒙^𝟐+𝒚^𝟐) ||
#20 || Newton’s backward interpolation formula || 18MAT21 ||
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) @𝟐(𝟏−𝒙), (𝟎.𝟓, 𝟏)
#17|| Finite Difference || Forward difference|| Backward difference || Difference table || 18MAT21||
Evaluate || lim_(𝒙→𝟏)(𝒙^(𝟏⁄(𝟏−𝒙)) )|| Differential Calculus ||
Rodrigues Formula & Results.
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 for p 𝒑^𝟐+𝟐𝒑𝒚𝒄𝒐𝒕𝒙=𝒚^𝟐
Express 𝒙^𝟑+𝟐𝒙^𝟐−𝟒𝒙+𝟓 in terms of Legendre polynomial
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).
Express 𝒇(𝒙)=𝒙^𝟒−𝟑𝒙^𝟑−𝒙^𝟐+𝟓𝒙 in terms of Legendre polynomial.
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.
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.
National Science Day-2024
Numerical Solution of the one dimensional Heat equation & working procedure.
Show that: 𝒊)𝑷_𝟐(𝒄𝒐𝒔𝜽)=1/4 (𝟏+𝟑𝒄𝒐𝒔𝜽), 𝒊𝒊) 𝑷_𝟑 (𝒄𝒐𝒔𝜽)=𝟏/𝟖 (𝟑𝒄𝒐𝒔𝜽+𝟓𝒄𝒐𝒔𝟑𝜽).
Express 𝟐𝒙^𝟑−𝒙^𝟐−𝟑𝒙+𝟐 in terms of Legendre polynomial
21MAT31:Numerical Method PDE, Classification of PDE of second order & Finite difference approximate.
#4 || Problem#3 || PDE || Eliminating the arbitrary constant || 𝒙^𝟐/𝒂^𝟐 +𝒚^𝟐/𝒃^𝟐 +𝒛^𝟐/𝒄^𝟐 =𝟏 ||
Evaluate the ( lim)_(x→0) [(1-cosx)/(xlog(1+x))] || Differential Calculus ||
Prove that : 𝑱((−𝟏)⁄𝟐) (𝒙)=√(𝟐/𝝅𝒙) 𝒄𝒐𝒔𝒙.
Series Solution of Legendre s Differential Equation
21MAT31: Numerical solution of the one dimensional wave equation.
Prove that : 𝑱(𝟏⁄𝟐) (𝒙)=√(𝟐/𝝅𝒙) 𝒔𝒊𝒏𝒙.
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.
Orthogonality of Bessel s Functions
Solve 𝝏𝒖/𝝏𝒕=(𝝏^𝟐 𝒖)/𝝏𝒙^𝟐, 𝒖=(𝟎,𝒕)=𝟎=𝒖(𝟏,𝒕), 𝒖(𝒙,𝟎)=𝒔𝒊𝒏𝝅𝒙 by taking h=0.2, (𝟎, 𝟎.𝟏)
#32 || Problem# 4 || Fit an interpolation polynomial || Newton’s Divided Difference || 18MAT21 ||
#3 || Problem#1 || Problem on joint distribution of two random variable X and Y || 18MAT41||
#10|| Complex line integration ||∫𝒅𝒛/(𝒛−𝒂)=𝟐𝝅𝒊 ||∫(𝒛−𝒂)^𝒏=𝟎 ||
#37 || Problem#3 || Lagrange's formula for interpolation || Numerical Methods || 18MAT21 ||
#16 || Problem#2 ||Solution of non-homogenous PDE by direct integration Solve: (𝝏^𝟐 𝒛)/𝝏𝒙𝝏𝒚=𝒙/𝒚+𝒂 ||
#4 || Problem#2 || Bilinear transformation || 𝒛=∞, 𝒊, 𝟎 𝐢𝐧𝐭𝐨 𝝎=−𝟏, −𝒊, 𝟏 || Fixed points ||
Evaluate || lim_(𝒙→𝟎)[𝟏𝒙^𝟐 −(𝒄𝒐𝒕)^𝟐 𝒙] || Differential Calculus ||
Working procedure for one dimensional wave equation
Find the numerical solution (𝝏^𝟐 𝒖)/𝝏𝒙^𝟐 =𝟐 𝝏𝒖/𝝏𝒕 , 𝒖=(𝟎,𝒕)=𝟎=𝒖(𝟒,𝒕), 𝒖(𝒙,𝟎)=𝒙(𝟒−𝒙) ,h=1,t=4 steps.
