From df9a499a56431f0b902705507a82975b06e4bcb0 Mon Sep 17 00:00:00 2001
From: Michael Wimmer <m.t.wimmer@tudelft.nl>
Date: Sun, 12 Sep 2021 20:34:29 +0000
Subject: [PATCH] Fix problem 5, add nonseparable example.
---
src/8_differential_equations_2.md | 6 +++---
1 file changed, 3 insertions(+), 3 deletions(-)
diff --git a/src/8_differential_equations_2.md b/src/8_differential_equations_2.md
index 4afb3fa..aa07d6b 100644
--- a/src/8_differential_equations_2.md
+++ b/src/8_differential_equations_2.md
@@ -574,11 +574,11 @@ necessary to work with numerical methods of solution.
$\frac{d^2}{dx^2}$ is Hermitian - you can thus directly assume that
the solutions form an orthogonal basis).
-5. [:smirk:] Take the partial differential equation
+5. [:smirk:] Consider the following partial differential equations, and try to make a separation ansatz $h(x,y)=f(x)g(y)$. What do you observe in each case? (Only attempt the separation, do not solve the problem fully)
- $$\frac{\partial h(x,y)}{\partial x} + x \frac{\partial h(x,y)}{\partial y} = 0. $$
+ (a) $$\frac{\partial h(x,y)}{\partial x} + x \frac{\partial h(x,y)}{\partial y} = 0. $$
- Try to make a separation ansatz $h(x,y)=f(x)g(y)$. What do you observe?
+ (b) $$\frac{\partial h(x,y)}{\partial x} + \frac{\partial h(x,y)}{\partial y} + xy\,h(x,y) = 0$$
6. [:sweat:] We consider the Hilbert space of functions $f(x)$ defined
for $x \ \epsilon \ [0,L]$ with $f(0)=f(L)=0$.
--
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