From b48d87b90af2b8b67f2aa260d858307f1fb6947f Mon Sep 17 00:00:00 2001
From: Michael Wimmer <m.t.wimmer@tudelft.nl>
Date: Sun, 12 Sep 2021 20:38:55 +0000
Subject: [PATCH] fix math errors
---
src/8_differential_equations_2.md | 12 ++++++------
1 file changed, 6 insertions(+), 6 deletions(-)
diff --git a/src/8_differential_equations_2.md b/src/8_differential_equations_2.md
index aa07d6b..2a6cc7b 100644
--- a/src/8_differential_equations_2.md
+++ b/src/8_differential_equations_2.md
@@ -536,13 +536,13 @@ necessary to work with numerical methods of solution.
1. [:grinning:] Which of the following equations for $y(x)$ is linear?
- (a) y''' - y'' + x \cos(x) y' + y - 1 = 0
+ (a) $y''' - y'' + x \cos(x) y' + y - 1 = 0$
- (b) y''' + 4 x y' - \cos(x) y = 0
+ (b) $y''' + 4 x y' - \cos(x) y = 0$
- (c) y'' + y y' = 0
+ (c) $y'' + y y' = 0$
- (d) y'' + e^x y' - x y = 0
+ (d) $y'' + e^x y' - x y = 0$
2. [:grinning:] Find the general solution to the equation
@@ -576,9 +576,9 @@ necessary to work with numerical methods of solution.
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)
- (a) $$\frac{\partial h(x,y)}{\partial x} + x \frac{\partial h(x,y)}{\partial y} = 0. $$
+ (a) $\frac{\partial h(x,y)}{\partial x} + x \frac{\partial h(x,y)}{\partial y} = 0. $
- (b) $$\frac{\partial h(x,y)}{\partial x} + \frac{\partial h(x,y)}{\partial y} + xy\,h(x,y) = 0$$
+ (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 $f(0)=f(L)=0$.
--
GitLab