From d04c11fea51178ef2e7e0ea2efb425cf1f455179 Mon Sep 17 00:00:00 2001 From: Leo Xu Date: Sat, 27 Dec 2025 12:24:30 +0800 Subject: [PATCH 1/5] fix: sol-foxtrot typo --- src/sol-foxtrot.typ | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/sol-foxtrot.typ b/src/sol-foxtrot.typ index 3db2e40..21dda96 100644 --- a/src/sol-foxtrot.typ +++ b/src/sol-foxtrot.typ @@ -157,7 +157,7 @@ Now we check the cases: So every lattice point is indeed a saddle point. - At any point of the form $(m + 1/2, n + 1/2)$, we have $A = C = pm pi^2$ and $B = 0$, - so $A C - B^2 = pi^4 < 0$. + so $A C - B^2 = pi^4 > 0$. Hence there are no saddle points here. == Solution to @exer-opt-geo (geometry optimization) From 7d2f115d9613eb94fe01f59518dba2f0d8d805d6 Mon Sep 17 00:00:00 2001 From: Leo Xu Date: Mon, 29 Dec 2025 11:39:55 +0800 Subject: [PATCH 2/5] fix: and -> an Not sure whether to use 'an' or 'a' - but I'm assuming people will read '=' as 'equals'. --- src/regions.typ | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/regions.typ b/src/regions.typ index 2fb5bd5..945e56b 100644 --- a/src/regions.typ +++ b/src/regions.typ @@ -92,7 +92,7 @@ The three that you should care about for this class are the following: ] - The *boundary* is usually the points you get when you choose any one of the $<=$ and $>=$ - constraints and turn it into and $=$ constraint. + constraints and turn it into an $=$ constraint. For example, the boundary of the region cut out by $-1 <= x <= 1$ and $-1 <= y <= 1$ (which is a square of side length $2$) are the four sides of the square, where either $x = pm 1$ or $y = pm 1$. From f6e2cf0e3e3f60a277afcd96ad81b023a8b9bc31 Mon Sep 17 00:00:00 2001 From: Leo Xu Date: Mon, 29 Dec 2025 14:07:14 +0800 Subject: [PATCH 3/5] fix: minor edit on opt This edit is motivated by the text after where the text introduces the four different limit cases. --- src/opt.typ | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/opt.typ b/src/opt.typ index 419e41f..e4ae2ed 100644 --- a/src/opt.typ +++ b/src/opt.typ @@ -66,7 +66,7 @@ Later on we'll do more examples where Step 2 and Step 3 are more intricate. so we're in the easy case and the recipe applies here. We check all the points in turn: - 0. $cal(R)$ has no boundary and limit cases when any variable approaches $0$ or $+oo$. + 0. $cal(R)$ has no boundary and limit cases when any variable approaches $0^+$ or $+oo$. 1. To find the critical points, calculate the gradient $ nabla f (x,y) = vec(1 - 8 / (x^2 y), 1 - 8 / (x y^2)) $ and then set it equal to $vec(0,0)$. From b336c84676ed272670e9e8c65c764ed7bd9f7948 Mon Sep 17 00:00:00 2001 From: Evan Chen Date: Mon, 29 Dec 2025 10:06:32 -0800 Subject: [PATCH 4/5] Update opt.typ --- src/opt.typ | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/opt.typ b/src/opt.typ index e4ae2ed..419e41f 100644 --- a/src/opt.typ +++ b/src/opt.typ @@ -66,7 +66,7 @@ Later on we'll do more examples where Step 2 and Step 3 are more intricate. so we're in the easy case and the recipe applies here. We check all the points in turn: - 0. $cal(R)$ has no boundary and limit cases when any variable approaches $0^+$ or $+oo$. + 0. $cal(R)$ has no boundary and limit cases when any variable approaches $0$ or $+oo$. 1. To find the critical points, calculate the gradient $ nabla f (x,y) = vec(1 - 8 / (x^2 y), 1 - 8 / (x y^2)) $ and then set it equal to $vec(0,0)$. From a3adc2a128a5efeae764f228aafce5478fd06b94 Mon Sep 17 00:00:00 2001 From: Evan Chen Date: Mon, 29 Dec 2025 10:07:52 -0800 Subject: [PATCH 5/5] Update opt.typ --- src/opt.typ | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/opt.typ b/src/opt.typ index 419e41f..e4ae2ed 100644 --- a/src/opt.typ +++ b/src/opt.typ @@ -66,7 +66,7 @@ Later on we'll do more examples where Step 2 and Step 3 are more intricate. so we're in the easy case and the recipe applies here. We check all the points in turn: - 0. $cal(R)$ has no boundary and limit cases when any variable approaches $0$ or $+oo$. + 0. $cal(R)$ has no boundary and limit cases when any variable approaches $0^+$ or $+oo$. 1. To find the critical points, calculate the gradient $ nabla f (x,y) = vec(1 - 8 / (x^2 y), 1 - 8 / (x y^2)) $ and then set it equal to $vec(0,0)$.