ODE Fall 2020 by F Khosh https://padlet.com/fkhosh/w8duyunkio5zkqfn Made with joy en-us 2020-07-22 22:08:58 UTC 2025-08-27 12:50:54 UTC hello@padlet.com Order 1 ODE fkhosh https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/660500388 1- y'=y
2- y'=x+3 (T&A)
3- y' = 4x^2 - 9
4- y' = y + x^3
5- y' = 2xy/lnx  
6-  y'/y = x^5

]]> 2020-07-22 23:08:12 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/660500388 Order 2 ODE fkhosh https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/660501023 1- xy''-y'=0
2- y'' + 3y' = 2
3-  y"= y' * y + x^2 : non linear ]]> 2020-07-22 23:09:19 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/660501023 homogeneous vs. non-homogeneous differential equations fkhosh https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/660501129 1-when y is a function of x
y'-y=x   non-homogeneous
y'-y=0 homogeneous

2- xy"+y'=x-3 non-homogenous
xy"'+y"=-x non- homogeneous (T&A)

3- 5y''' + 2y'' - 3y' + y=0 homogenous
  y'-y = x + 5 non- homogeneous

4- 
Homogenous: 
Non-Homogenous: ]]> 2020-07-22 23:09:31 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/660501129 PDE or ODE fkhosh https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/660506044 2020-07-22 23:18:00 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/660506044 Linear vs. non-linear fkhosh https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/679607953 1- linear : xy'+y/ln(x) = sinx
non-linear : y y"= e^x
2- 
linear: y'''+y''/2x+y-x = arctan(x)
non-linear: y'^5*y^3 = Ln lxl
3- linear: y' - ln(x)=0
4- non-linear: (y''(3x^2))/y' + y = x^2


]]> 2020-08-13 23:02:06 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/679607953 PDE or ODE tinochiggs7 https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/680235291 2020-08-14 13:29:46 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/680235291 Special Symbols https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/680239859 Partial Differ: ∂

]]> 2020-08-14 13:32:47 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/680239859 Add a list of Theorems and concepts you have learned on 1st order and 2nd order ODEs that might apply to nth order, too. fkhosh https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/737651265 1- Wronskian]]> 2020-09-11 03:14:35 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/737651265 2 - Initial conditions (more than 2) https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/739016049 2020-09-11 15:07:43 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/739016049 3- linearity and homogeneos. https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/739025973 2020-09-11 15:09:47 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/739025973 https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/741464057 4 - existence and uniqueness THM for linear homogenous ODEs]]> 2020-09-13 04:17:04 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/741464057 tinochiggs7 https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/742584458 5. We can use the idea of Linear operators to work through the problem solving. I do not know if we have also talked about the linear independence concept yet]]> 2020-09-14 02:09:53 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/742584458 6. Linear and non-homogenous general solution. https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/743476771 2020-09-14 11:41:31 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/743476771 https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/745160918 7. Variation of Parameters on higher order ODE's]]> 2020-09-14 17:48:45 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/745160918 What is your intuition of determinant and eigen value or your understanding of your google search? fkhosh https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/750354514 2020-09-16 03:25:51 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/750354514 Eigenvector (Antonio) https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/751780829 An eigenvector is a vector that does not change when a transformation is applied to it. It becomes a scaled version of the original vector. This scalar value is known as the eigen value. ]]> 2020-09-16 14:36:57 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/751780829 Eigenvalues and eigenvectors(Tea?No!) tinochiggs7 https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/751784751 Eigenvalues can help us determine how a system develops over time, think of Antonio's presentation as an example ]]> 2020-09-16 14:37:47 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/751784751 Determinant of a matrix is a special number that can be calculated from a square matrix , which has the number of rows equal to the number of columns. Eigen values are vectors (scalar properties) https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/751794980 2020-09-16 14:39:54 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/751794980 Eigen values (Sumin) https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/751796638 Eigen values are scalars associated with a linear system of equations, also known as characteristic roots.]]> 2020-09-16 14:40:16 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/751796638 Eigen Values https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/751800498 Applying Eigen values to 2 x 2 matrix will result in the matrix tuning into [a-(lambda_1) b ; c d-(lambda_2)]. From this you able to solve for lambda_1 and lambda_2.]]> 2020-09-16 14:41:06 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/751800498 Determinants and Eigenvalues https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/751803086 The determinant is the product of eigenvalues.

det(A) =  λ1 · λ2 · · · · · λn ]]> 2020-09-16 14:41:41 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/751803086 Eigenvalue - Feven https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/751813201 Eigenvalue is a number telling us how much variance there is in the data in that direction /or how spread out the data is on that line. ]]> 2020-09-16 14:43:44 UTC https://padlet.com/fkhosh/w8duyunkio5zkqfn/wish/751813201