Q1. Find affox and af/ày. f(x,y) = x2 + 5xy + sin x + 7e* (4 marks)
Given f(x,y) = 2y + 3y + yin(x) + x, find af ах +5 X af — 12ух -7+езу, у +1 ах af = 2ух -6+ у ах Х Од у 1 = 2ух -6+ ах Х о af 12ух-74У +1 ах Х
,y)-3x2-5xy + y2 find F 3. or the function (x a) f (x, y) b) fy,(xr, y) c) f(x, y) ,y)-3x2-5xy + y2 find F 3. or the function (x a) f (x, y) b) fy,(xr, y) c) f(x, y)
find fxx(x,y), fxy(x,y), fyx(x,y) and fyy(x,y) for the function f. f(x,y)=8xe^5xy 19. Find fxx (x,y), fxy(x,y), fyx(x,y), and fyy(x,y) for the function f. f(x,y) = 8x e 5xy fx(x,y)= fxy(x,y)= fyx (x,y) = fyy(x,y) =
Problem 3 (hand-calculation): Consider a two-dimensional function: f(x, y)- sin(x)cos() where x and y are in radi ans (a) Evaluate a f/oz, f / ду, and /(8z0) at x = y = 1 analytically. (b) Evaluate af/az. Э//ду, and Эг f/0гду) at x = y = 1 numerically using 2nd-order central difference formula with a grid spacing h -0.1. Take a photo of your work. Include all pages in a single photo named problem3.jpg. Set the following in your homework...
(1 point) Find the solution of xy" + 5xy' + (4 + 1x)y = 0, x > 0 of the form Yi = x n=0 where co = 1. Enter r = -2 Cn = - n= 1,2,3,...
Әf Əf HW: #1. Find the expressions for af of - and om I in terms of адх” ду дz. x = p sino cos 0; y = psin o sin 0; z = pcosø. , where do and of #2. Express V? f in spherical coordinates, where f(0,0,0) is a scalar function.
Consider the differential equation (1-x²)y" - 5xy' - 3 y = 0 1. Find its general solution y = Xar, x" in the form y = doy1(x) + anyz(x), where yı(x) and y2(x) are power series 2. What is the radius of convergence for the series yı(x) and y(x)?
5. Find the derivative matrices of the following composition of functions. (а) fog where f (x, у) — 2х — 3у, g(u, v) - (usin u, U sin u) (Ъ) f.g where f(х, у, 2) %3D (x? + у? +2?,х— у+2:), g() %3 (2, 13, 2/4) (с) fog wherе f (x, у, z) 3D (хуz, ху + xz — yz) where g(u, v, w) %3D (uu, uw, vw) 5. Find the derivative matrices of the following composition of functions. (а)...
solve k2 Solve the following partial differential equation by Laplace transform: д?у ду dx2 at , with the initial and boundary conditions: t = 0, y = A x = 0, y = B[u(t) – uſt - to)] x = 0, y = 1 5 Where, k, A, B and to are constants