Intro to L A T E X Intro to Beamer Geometric Analysis A Proof A Guide to Presentations in L A T E X-beamer with a detour to Geometric Analysis Eduardo Balreira Trinity University Mathematics Department Major Seminar, Fall 2008 Balreira Presentations in L A T E X
40
Embed
A Guide to Presentations in LaTeX-beamer - with a …ramanujan.math.trinity.edu/tumath/students/latex/Beamer_Template...Intro to LATEX Intro to Beamer Geometric Analysis A Proof A
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
A Guide to Presentations in LATEX-beamer
with a detour to Geometric Analysis
Eduardo Balreira
Trinity UniversityMathematics Department
Major Seminar, Fall 2008
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
Outline
1 Intro to LATEX
2 Intro to Beamer
3 Geometric Analysis
4 A Proof
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
Some Symbols
LaTeX is a mathematics typesetting program.
Standard Language to Write Mathematics
(M2, g) ↔ $(M^2,g)$
∆u − K (x) − e2u = 0 ↔ $\Delta u -K(x) - e^2u = 0$
infn∈N
1
n
= 0
$\ds\inf_n\in\mathbbN\set\dfrac1n=0$
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
Compare displaystyle
∑∞n=1
1n2 =
π2
6versus
∞∑
n=1
1
n2=
π2
6
$\sum_n=1^\infty\frac1n^2=\dfrac\pi^26$
and
$\ds\sum_n=1^\infty\frac1n^2=\frac\pi^26$
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
Common functions
cos x → $\cos x$
arctan x → $\arctan x$
f (x) =√
x2 + 1 → $f(x) = \sqrtx^2+1$
f (x) = n√
x2 + 1 → $f(x) = \sqrt[n]x^2+1$
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
Theorems - code
Theorem (Poincare Inequality)
If |Ω| < ∞, then
λ1(Ω) = infu 6=0
|∇u|22‖u‖2
> 0
is achieved.
\beginthm[Poincar\’e Inequality]
If $|\Omega| < \infty$, then
\[
\lambda_1(\Omega) =
\inf_u\neq 0 \dfrac|\nabla u|^2_2\|u\|^2 > 0
\]
is achieved.
\endthm
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
Example - Arrays
−∆u + λu = |u|p−2, in Ωu ≥ 0, u ∈ H1
0 (Ω)
$\left\
\beginarraycccc
-\Delta u +\lambda u &= & |u|^p-2, &\textrm in
\Omega \\
u &\geq & 0, & u\in H_0^1(\Omega)
\endarray
\right.$
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
Example - ArraysChange centering
−∆u + λu = |u|p−2, in Ωu ≥ 0, u ∈ H1
0 (Ω)
$\left\
\beginarraylcrr
-\Delta u +\lambda u &= & |u|^p-2, &\textrm in
\Omega \\
u &\geq & 0, & u\in H_0^1(\Omega)
\endarray
\right.$
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
Example - ArraysChange centering
−∆u + λu = |u|p−2, in Ωu ≥ 0, u ∈ H1
0 (Ω)
$\left\
\beginarrayrcll
-\Delta u +\lambda u &= & |u|^p-2, &\textrm in
\Omega \\
u &\geq & 0, & u\in H_0^1(\Omega)
\endarray
\right.$
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
More Examples
ϕ(u) =
∫
Ω
[‖∇u‖2
2+ λ
u2
2− (u+)p
p
]
dµ
$\ds \varphi (u) = \int_\Omega \left[
\dfrac\|\nabla u\|^22 +
\lambda\dfracu^22 -
\dfrac(u^+)^pp \right] d\mu $
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
Even More Examples
De Morgan’s Law(
n⋃
i=1
Ai
)c
=n⋂
i=1
Aci
$\ds \left(\bigcup_i=1^n A_i\right)^c =
\bigcap_i=1^n A_i^c$
A × B = (a, b)|a ∈ A, b ∈ B
$A\times B = \set(a,b)|a\in A, b\in B$
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
Equations
Consider the equation of Energy below.
E (u) =
∫
|∇u|2dx (1)
This is how we refer to (1).
\beginequation\labeleq:energy
E(u) = \int |\nabla u|^2 dx
\endequation
This is how we refer to \eqrefeq:energy.
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
Equations
Consider the equation without a number below.
E (u) =
∫
|∇u|2dx
\beginequation\labeleq:energy
E(u) = \int |\nabla u|^2 dx \nonumber
\endequation
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
EquationsTag an equation
Consider the equation with a tag
E (u) =
∫
|∇u|2dx (E)
If u is harmonic, (E) is preserved.
\beginequation\labeleq:energytag
E(u) = \int |\nabla u|^2 dx \tagE
\endequation
If $u$ is harmonic, \eqrefeq:energytag is preserved.
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
Equationsin an array
Consider the expression below
(a + b)2 = (a + b)(a + b)
= a2 + 2ab + b2(2)
\beginequation
\beginsplit
(a+b)^2 & = (a+b)(a+b) \\
& = a^2 +2ab +b^2
\endsplit
\endequation
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
Environments
In LaTeX, environments must match:
\begin...
.
.
.
\end...
$ ...$ → for math symbols
\[ ... \] → for centering expressions
\left( ... \right) → match size of parentheses
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
Environmentsdelimiters
(
∫
|∇u|pdµ)p versus
(∫
|∇u|pdµ
)p
$(\ds\int|\nabla u|^p d\mu)^p$
$\left(\ds\int|\nabla u|^p d\mu\right)^p$
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof
Tables
Consider the truth table:
P Q ¬P ¬P → (P ∨ Q)
T T F TT F F TF T T TF F T F
Balreira Presentations in LATEX
Intro to LATEX Intro to Beamer Geometric Analysis A Proof