MmTeX Demo 02 - Mathematics

1 Simple examples

Some inline math: $-3xy+5a_z^{x^2+1}+9(u+w)$ . Some block math:

$$a^2+b^2=c^2$$

(1)

2 More complex examples

Fraction:

$$\frac{1}{1+x}$$

(2)

Fraction and root:

$$\sqrt{\frac{3x-8}{x^2+y^2}}$$

(3)

Integral:

$$\underset{0}{\overset{1}{\int }}\frac{x}{1+x^2}dx$$

(4)

Inline Integral: ${\int }_a^{y^2}f\left(x\right)dx$ .

Sum:

$$\sum _{n=0}^{\infty }\frac{a_n}{n^2}$$

(5)

Limit:

$$\underset{N\to \infty }{lim}\sum _{n=0}^N\frac{x^n}{n!}=e^x$$

(6)

\nolimits command:

$${\int }_0^1\frac{x}{1+x^2}dx{\int }_{-\pi }^{\pi }f\left(x\right)sin\left(x\right)dx$$

(7)

\left...\right constructs:

$${1+\frac{1}{x}|}_{-1}^{X^2}{1+\frac{1}{x}|}_1^2$$

(8)

3 Spaces

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4 Vectors and Matrices

Vectors:

$$\overrightarrow{a}=\left(\begin{array}{c}-4\\ 5\\ 0\end{array}\right),\overrightarrow{b}=\left(\begin{array}{c}4x\\ 3y\\ x+y\end{array}\right)$$

(9)

A matrix:

$$A=\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right)$$

(10)