Part of a series of lectures to be delivered on typesetting documents and presentations with LaTeX. Provided as a Creative Commons Document

1. Basics Typesetting Math rich tables
Typesetting Mathematics in LaTeX
Getting your hands dirty
Suddhasheel Ghosh
1 Department of Civil Engineering
MGM’s Jawaharlal Nehru Engineering College,
Aurangabad, MH
2 MGM
- Institute of Biosciences and Technology
Aurangabad, MH
The LaTeX workshop
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Mathematics

2. Basics Typesetting Math rich tables
Outline
1
Preliminary commands
2
Inline and display math
Setting up equations
Step-wise functions or case based functions
Matrices and determinants
3
Math rich tables
shudh
Mathematics

3. Basics Typesetting Math rich tables
Outline
1
Preliminary commands
2
Inline and display math
Setting up equations
Step-wise functions or case based functions
Matrices and determinants
3
Math rich tables
shudh
Mathematics

4. Basics Typesetting Math rich tables
Preamble settings
Necessary requirement for typesetting math
In the preamble, set the following
usepackage{amssymb, amsmath}
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Mathematics

5. Basics Typesetting Math rich tables
Basic commands
It is necessary to enclose all math by the $ sign.
n
$sum_{i=1}^n
a_n x^n = 0$
an xn = 0
i=1
n
$prod_{i=1}^n
a_n x^n = 1$
an xn = 1
i=1
$int x^n dx =
frac{x^{n+1}}{n+1}$
xn dx =
∞
xn dx =
$int_0^infty x^n dx =
frac{1}{n+1} left[
x^{n+1}right]_0^infty$
0
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1
xn+1
n+1
4
2
${4}choose{2}$
Mathematics
xn+1
n+1
∞
0

6. Basics Typesetting Math rich tables
Our greeky friends
The small ones:
alpha, beta, gamma, dots, chi, pi, phi, psi, xi
provide:
α, β, γ, . . . , χ, π, φ, ψ, ξ
On the other hand, the capital ones:
A, B, gamma, dots, X, pi, phi, psi, xi
provide:
A, B, Γ, . . . , X, Π, Φ, Ψ, Ξ
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Mathematics

7. Basics Typesetting Math rich tables
Our wonderful roots
The Euclidean distance between two points $mathbf{p}
(x_1, y_1)$ and $mathbf{q}(x_2,y_2)$ is given by:
$$ d(mathbf{p}, mathbf{q}) = sqrt{(x_1-x_2)^2
+ (y_1 - y_2)^2}$$
and the Minkowski’s distance with the $p$-norm is given as
$$d_p(mathbf{p}, mathbf{q}) = sqrt[p]{vert x_1-x_2
vert ^p + vert y_1 - y_2 vert ^p}$$
produces:
The Euclidean distance between two points p(x1 , y1 ) and
q(x2 , y2 ) is given by:
d(p, q) =
(x1 − x2 )2 + (y1 − y2 )2
and the Minkowski’s distance with the p-norm is given as
dp (p, q) =
p
|x1 − x2 |p + |y1 − y2 |p
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Mathematics

8. Basics Typesetting Math rich tables
Symbols we love
±
∀
⊃
≤
≥
∼
≡
∩
×
→
←
¯
x
pm
forall
supset
le
ge
sim
nsim
equiv
cap
times
ll
rightarrow
leftarrow
bar{x}
∈
⊂
≈
∪
÷
⇒
⇐
x
mp
in
subset
nleq
ngeq
approx
napprox
nequiv
cup
div
gg
Rightarrow
Leftarrow
vec{x}
All symbols require math mode. The math expressions must
be surrounded by the $ sign on both sides.
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Mathematics

9. Basics Typesetting Math rich tables
That’s the limit !
$lim_{x rightarrow 5} frac{x^2 - 25}{x - 5} = 10$
produces:
x2 − 25
= 10
x→5 x − 5
lim
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Mathematics

10. Basics Typesetting Math rich tables
Equations Cases Matrices and determinants
Outline
1
Preliminary commands
2
Inline and display math
Setting up equations
Step-wise functions or case based functions
Matrices and determinants
3
Math rich tables
shudh
Mathematics

11. Basics Typesetting Math rich tables
Equations Cases Matrices and determinants
Typesetting math
Inline and display modes
The equation of a straight line is given by $y = m x + c$, where $m$
denotes the slope, and $c$ denotes the $y$-intercept.
produces:
The equation of a straight line is given by y = mx + c, where m
denotes the slope, and c denotes the y-intercept.
The Fourier transform of a function $f:mathbb{R}rightarrow
mathbb{C}$ is given by:
$$
hat f(xi) = int_{-infty}^{infty} f(x) e^{-2pi i x xi} dx
$$
produces:
The Fourier transform of a function f : R → C is given by:
∞
ˆ
f (ξ) =
f (x)e−2πixξ dx
−∞
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Mathematics

12. Basics Typesetting Math rich tables
Equations Cases Matrices and determinants
Typesetting math
Equations
begin{equation}
sum_{i=0}^n a_i cos theta + b_i sin theta
= mathcal{F}
end{equation}
n
ai cos θ + bi sin θ = F
i=0
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Mathematics
(1)

13. Basics Typesetting Math rich tables
Equations Cases Matrices and determinants
Typesetting math
Piecewise functions or case based functions
$$
f(x) =
begin{cases}
0 & xinmathbb{Q}
1 & xinmathbb{I}
end{cases}
$$

0


f (x) = 
1

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Mathematics
x∈Q
x∈I

14. Basics Typesetting Math rich tables
Equations Cases Matrices and determinants
Typesetting math
Matrices
$$
begin{bmatrix}
1 &2 &3 &4
6 &7 &9 &10
5 &6 &3 &1
4 &2 &8 &2
end{bmatrix}
begin{bmatrix}
x y z t
end{bmatrix}
=
begin{bmatrix}
4 5 5 2
end{bmatrix}
$$

1


6



5




4
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Mathematics
2
7
6
2
   
3 4  x 4
   
   
   
9 10 y 5
  =  
   
   
3 1  z 5
   
   
   
8 2 t
2

15. Basics Typesetting Math rich tables
Equations Cases Matrices and determinants
Typesetting math
Determinants
$$
begin{vmatrix}
1 & 2 & 3
4 & 5 & 6
7 & 8 & 9
end{vmatrix}
= 0
$$
1 2 3
4 5 6 =0
7 8 9
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Mathematics

16. Basics Typesetting Math rich tables
Outline
1
Preliminary commands
2
Inline and display math
Setting up equations
Step-wise functions or case based functions
Matrices and determinants
3
Math rich tables
shudh
Mathematics

17. Basics Typesetting Math rich tables
Tables with mathematical expressions
begin{table}
begin{tabular}{|c|l|c|l|}
hline
S. No. &Type &Degree
&Expression
hline
S. No.
1 & Algebraic & 1 & $x$
1
hline
2
2 &Algebraic &2
3
&$x^2 + x + 1$
hline
3 &Algebraic &3
&$x^3 + x^2 + x + 1$
hline
end{tabular}
end{table}
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Type
Algebraic
Algebraic
Algebraic
Mathematics
Degree
1
2
3
Expression
x
x2 + x + 1
x3 + x2 + x + 1