commit 73568521e9e777443b7149310ae4e7207dfd559e parent 90dd6387259c0c8110a947aec344a79b065c2132 Author: miksa234 <milutin@popovic.xyz> Date: Wed, 2 Mar 2022 10:58:49 +0100 last commit Diffstat:
20 files changed, 3 insertions(+), 5 deletions(-)
diff --git a/appl_ana/assingments/Exercises3.pdf b/appl_ana/assingments/Exercises3.pdf Binary files differ. diff --git a/appl_ana/assingments/ApplAnalysis-exercise1-P1-3.pdf b/appl_ana/assingments/ass1.pdf Binary files differ. diff --git a/appl_ana/assingments/AppliedAnalysis_2021-exercise_.pdf b/appl_ana/assingments/ass2.pdf Binary files differ. diff --git a/appl_ana/assingments/AppAnalysis-exercise3.pdf b/appl_ana/assingments/ass3.pdf Binary files differ. diff --git a/appl_ana/assingments/Exercises1.pdf b/appl_ana/assingments/ass4.pdf Binary files differ. diff --git a/appl_ana/assingments/Exercises2.pdf b/appl_ana/assingments/ass5.pdf Binary files differ. diff --git a/appl_ana/assingments/Exercises2.pdf b/appl_ana/assingments/ass6.pdf Binary files differ. diff --git a/appl_ana/assingments/Exercises4.pdf b/appl_ana/assingments/ass7.pdf Binary files differ. diff --git a/appl_ana/assingments/Exercises5.pdf b/appl_ana/assingments/ass8.pdf Binary files differ. diff --git a/appl_ana/jan25ana/ex1_1.png b/appl_ana/jan25ana/ex1_1.png Binary files differ. diff --git a/appl_ana/jan25ana/ex1_2.png b/appl_ana/jan25ana/ex1_2.png Binary files differ. diff --git a/appl_ana/jan25ana/ex1_3.png b/appl_ana/jan25ana/ex1_3.png Binary files differ. diff --git a/appl_ana/jan25ana/ex2_1.png b/appl_ana/jan25ana/ex2_1.png Binary files differ. diff --git a/appl_ana/jan25ana/ex2_2.png b/appl_ana/jan25ana/ex2_2.png Binary files differ. diff --git a/appl_ana/jan25ana/ex3_1.png b/appl_ana/jan25ana/ex3_1.png Binary files differ. diff --git a/appl_ana/jan25ana/ex3_2.png b/appl_ana/jan25ana/ex3_2.png Binary files differ. diff --git a/appl_ana/jan25ana/ex3_3.png b/appl_ana/jan25ana/ex3_3.png Binary files differ. diff --git a/appl_ana/jan25ana/ex3_4.png b/appl_ana/jan25ana/ex3_4.png Binary files differ. diff --git a/appl_ana/sesh2/main.pdf b/appl_ana/sesh2/main.pdf Binary files differ. diff --git a/appl_ana/sesh2/main.tex b/appl_ana/sesh2/main.tex @@ -219,11 +219,9 @@ The ODE then expands to \eps^0(y_0' + y_0) + \eps(y_1' + y_1 - y_0^2) + \eps^2(y_2' + y_2 - 2y_0y_1) + O(\eps^3) = 0. \end{align} -Equations in order of $\eps$ and $\eps^2$ are non homogeneous ODE's, a little -bit of a hassle to solve but, still easy by first solving the non homogeneous -part, getting a constant dependent on $x$ we can plug the solution into the -non homogeneous equation and calculate for the constant (...). The solution to -these three coefficients with the boundary conditions $y_0(0) = 1$, $y_1(0) = +Equations in order of $\eps$ and $\eps^2$ are non-homogeneous ODE's. The +solution to these three coefficients with the boundary conditions $y_0(0) = +1$, $y_1(0) = y_2(0) = 0$ we get \begin{align} y_0 = e^{-x}, \;\;\;\; y_1 = -e^{-2x} + e^{-x}, \;\;\;\; y_2 = e^{-3x} -