Do math typesetting in one markdown file using KaTeX

Chinese version: Zhihu

Use Vs Code and extension Markdown Preview Enhanced (by Yiyi Wang) you can preview math typesetting in markdown file using KaTeX, see Math.

By the way, I use Markdown All in One (by Yu Zhang) to creat table of contents and export markdown to html, Markdown Footnote (by Mai Hou) to automatically add footnotes and markdown-index (by legendmohe) to automatically add serial numbers on titles.

Here I introduce some basic fomulas most used in Calculus, for more information, see KaTeX.

The contents in every section are: code, preview.

1. Accents

1.1. Prime

$ f'(x) $
$f'(x)$

1.2. Vector

$ \vec {a} $
$\vec {a}$

$ \overrightarrow {PP_0} $
$\overrightarrow {PP_0}$

1.3. Hat

$ \hat{\theta} $
$\hat{\theta}$

$ \widehat{ac} $
$\widehat{ac}$

2. Delimiters

2.1. Parentheses

$ (x) $
$(x)$

2.2. Brackets

$ [x] $
$[x]$

2.3. Braces

$ \{x\} $
$\{x\}$

2.4. Absolute Value

$ |x| $
$|x|$

2.5. Delimiter Sizing

( \big( \Big( \bigg( \Bigg( $( \big( \Big( \bigg( \Bigg($

$ (\csc x)' = \Big ( \frac {1} {\sin x} \Big )' $
$(\csc x)' = \Big ( \frac {1} {\sin x} \Big )'$

$ \frac {d^2f} {dx^2} \big | _{x=x_0} $
$\frac {d^2f} {dx^2} \big | _{x=x_0}$

3. Environments

3.1. Piecewise Function

$ f(x) = \begin{cases} x, &\text{if } x \ge 0 \\ -x, &\text{if } x < 0 \end{cases} $

$$f(x) = \begin{cases} x, &\text{if } x \ge 0 \\ -x, &\text{if } x < 0 \end{cases}$$

3.2. Vmatrix

$ \begin{vmatrix} a & b \\ c & d \end{vmatrix} $

$$\begin{vmatrix} a & b \\ c & d \end{vmatrix}$$

4. Layout

4.1. Line Breaks

$ a b \\ c d $
$a b \\ c d$

5. Greek Letters

5.1. alpha

$ \alpha $
$\alpha$

5.2. beta

$ \beta $
$\beta$

5.3. Delta

$ \Delta $
$\Delta$

5.4. theta

$ \theta $
$\theta$

5.5. lambda

$ \lambda $
$\lambda$

5.6. mu

$ \mu $
$\mu$

5.7. xi

$ \xi $
$\xi$

5.8. pi

$ \pi $
$\pi$

5.9. Partial Derivative

$ \partial $
$\partial$

6. Binary Operators

6.1. Plus

$ x + y $
$x + y$

6.2. Minus

$ x - y $
$x - y$

6.3. Times

$ x \times y $
$x \times y$

6.4. Divide

$ x \div y $
$x \div y$

6.5. Intersect

$ (0,5) \cap (-1,3) $
$(0,5) \cap (-1,3)$

6.6. Union

$ (-\infty,0) \cup (0,+\infty) $
$(-\infty,0) \cup (0,+\infty)$

7. Vertical Layout

7.1. Superscript

$ e^x $
$e^x$

7.2. Subscript

$ x_n $
$x_n$

8. Spacing

$ a b \\ a \space b $
$a b \\ a \space b$

or

$ a b \\ a \ b $
$a b \\ a \ b$

9. Logic and Set Theory

9.1. in

$ k \in \bf {Z} $
$k \in \bf {Z}$

9.2. subset

$ D \subset R $
$D \subset R$

10. Big Operators

10.1. Integration

$ \int _{-\infty} ^{+\infty} e^x dx $
$\int _{-\infty} ^{+\infty} e^x dx$

$ \iint \limits _D f(x,y) dxdy $
$\iint \limits _D f(x,y) dxdy$

10.2. Sum

$ \sum \limits _{i=1} ^n f(x) $
$\sum \limits _{i=1} ^n f(x)$

$ \sum \limits _{\substack {0<i<m \\ 0<j<n}} f(x) $
$\sum \limits _{\substack {0<i<m \\ 0<j<n}} f(x)$

10.3. Product

$ \prod \limits _{k=1} ^n a_k $
$\prod \limits _{k=1} ^n a_k$

11. Fractions

$ \frac {x^2} {x+1} $
$\frac {x^2} {x+1}$

$ \frac {a} {1 + \frac {1} {b}} $
$\frac {a} {1 + \frac {1} {b}}$

12. Math Operators

12.1. sin

$ \sin x $
$\sin x$

12.2. cos

$ \cos x $
$\cos x$

12.3. tan

$ \tan x $
$\tan x$

12.4. arcsin

$ \arcsin x $
$\arcsin x$

12.5. arctan

$ \arctan x $
$\arctan x$

12.6. lg

$ \lg x $
$\lg x$

12.7. ln

$ \ln x $
$\ln x$

12.8. log

$ \log x $
$\log x$

12.9. Radical Sign

$ \sqrt x $
$\sqrt x$

$ \sqrt [3] {x^2+2x+1} $
$\sqrt [3] {x^2+2x+1}$

12.10. lim

$ f'(x) = \lim \limits _{\Delta x \rightarrow 0} \frac {f(x + \Delta x) - f(x)} {\Delta x} $

$f'(x) = \lim \limits _{\Delta x \rightarrow 0} \frac {f(x + \Delta x) - f(x)} {\Delta x}$

13. Relations

13.1. equal to

$ x = y $
$x = y$

13.2. not equal to

$ x \ne y $
$x \ne y$

13.3. less than

$ x < y $
$x < y$

13.4. greater than

$ x > y $
$x > y$

13.5. less than or equal to

$ x \le y $
$x \le y$

13.6. greater than or equal to

$ x \ge y $
$x \ge y$

13.7. equivalent to

$ F(x,f(x)) \equiv 0, x \in D $
$F(x,f(x)) \equiv 0, x \in D$

13.8. approximately equal to

$ x \approx y $
$x \approx y$

14. Arrows

14.1. right arrow

$ x \rightarrow 0 $
$x \rightarrow 0$

14.2. not right arrow

$ x \nrightarrow 0 $
$x \nrightarrow 0$

14.3. Long Equal

$ 2^{\frac 1 x} \xlongequal {y = \frac 1 x} 2^y $
$2^{\frac 1 x} \xlongequal {y = \frac 1 x} 2^y$

15. Font

15.1. Bold

$ R \ \ \bf R $
$R \ \ \bf R$

16. Symbols and Punctuation

16.1. Infinity

$ \infty $
$\infty$

16.2. Dots

$ \dots $
$\dots$

16.3. Dot Product

$ x \sdot y $
$x \sdot y$