Recent content by oxxiissiixxo

dx/dt=ay and dy/dt=bx where x and y are function of t [x(t) and y(t)] and a and b are constant. 1) show what x and y satisfy the equation for a hyperbola: y^2-(b/a)*x^2=(y_0)^2-(b/a)*(x_0)^2 2) suppose at some time t_s, the point (x(t_s),y(t_s)) lies on the upper branch of hyperbola, show...

when x goes very large, say infinite, what does this equation will look like? H is a constant 1) 1/(1+(x/H)^2)^(1/2)) 2) 1/(1+(H/x)^2)^(1/2)) The answers are 1) 1/x^2 2) 1/x But I am not too sure how to get there. Thank you

Is this correct? ∑_ j A_ji dot A_ij dot x_j = ∑_ i A_ij^T dot b_i ?

I found out that the solution for ∇∙(φuu) is φu∙∇u+u[∇∙(φu)] for this the solution is just seemed like ∇∙(φuu) is φu∙∇u+u[∇∙(φu)] ∇∙(AB) is A∙∇B+B[∇∙(A)] but I just can't fill in the step correctly in between and ∇∙(T×u) is -u×(∇∙T)+T

I want to make sure the way I am writing this A^T dot A dot x = A^T dot b in index notation correctly. Would you mind to do that one time for me so that I can match up with my answer? My answer was A^T dot A dot x = A^T dot b >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>...

w=∇×u Is this correct? w_i=ε_ijk ∂/(∂x_j ) u_k w and u are the vectors C=(x∙y)z Is this correct? C_i= ∑_i〖(x_i y_j)∙z_i 〗 C, x, y, z are vectors A^T∙A ∙x=A^T∙b Is this correct...

How can I expand this term ∇∙(φuu) and ∇∙(T×u) ∇∙(φuu) where φ is a scalar and u is a vector and ∇∙(T×u) where T is a second order tensor and u is a vector.

Can any show me how you will go about proofing this identity ∇×(u×v)=v∙∇u-u∙∇v+u∇∙v-v ∇∙u where v and u are vectors Many thanks.

Please show me the way the proof this! div (u cross v) = v dot grad (u)- u dot grad(v) where v and u is a vector. The product rule doesn't seem working

I am doing the finite differencing for a pde and I am trying to expand the term f_m+1 with a superscript n+1 around say (f_m with a superscript n) to see whether or not the pde is consistent. For forward in time, a partial derivative of time (df/dt)will be rewrite as [(f_m with a superscript...

Homework Statement how to do taylor expansion for fm+1n+1; f(t,x) with sub script m+1 and a super script n+1 Homework Equations I know how to do taylor expansion for fm+1 and fn+1, but not fm+1n+1 The Attempt at a Solution

Homework Statement Convert to standard form ODE system y0 = f(t, y): t^2y'' + sin(y') + 2y − 1 = 0 the goal is to reduce the equation above to be a first order ode. Homework Equations The Attempt at a Solution I tried to introduced a new variable but the sin(y') seems tricky.

Homework Statement The questions are in the attachment. please help! Homework Equations M term is the diffusion. The Attempt at a Solution for the right hand side terms, it is just adding another velocity term, however on the left hand side term, i dun understand y there will be a...

Homework Statement Show (in complete detail) that X is a full column rank matrix if and only if X^TX is non-singular (invertible). Assume X is a real matrix. X^T is X transpose Homework Equations The Attempt at a Solution

Thanks Man anyway. You are my big help.