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#151 2022-08-18 00:12:55

zetafunc
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Registered: 2014-05-21
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Re: LaTeX - A Crash Course

You can also type the pi symbol in text form by typing the following:

:pi

which produces π.

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#152 2022-11-02 11:51:26

Temporary username
Member
Registered: 2022-11-02
Posts: 5

Re: LaTeX - A Crash Course

i found a broken latex post,

I couldn't fix it

Last edited by Temporary username (2022-11-02 11:52:17)

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#153 2022-11-02 14:08:30

Temporary username
Member
Registered: 2022-11-02
Posts: 5

Re: LaTeX - A Crash Course

Temporary username wrote:

i found a broken latex post,

x^{2}+y^{2}=100\ \left\{x<10-\frac{y}{\sqrt{3}}\right\}\left\{y<\frac{159}{16}\right\}\left\{14x+8y>-160\right\}
x^{2}+\left(y+7\right)^{2}=5
\left(x-6\right)^{2}+\left(y+4\right)^{2}=5
\left(x-15\right)^{2}+\left(y-5\sqrt{3}\right)^{2}=100\left\{x<10-\frac{y}{\sqrt{3}}\right\}
x^{2}+\left(y-8\right)^{2}=5\ \left\{y<\frac{159}{16}\right\}
\left(x+6\right)^{2}+\left(y-4\right)^{2}=5
\left(x+7\right)^{2}+\left(y+4\right)^{2}=5\left\{14x+8y>-160\right\}
x^{2}+y^{2}=18
x^{2}+\left(y+2\right)^{2}=4
\left(x-3\right)^{2}+\left(y-3\right)^{2}=4
\left(x+4\right)^{2}+y^{2}=4
y=2x+8\left\{-5<y<6\right\}\left\{\left(x+7\right)^{2}+\left(y+4\right)^{2}>5\right\}
\left(x+y-7\right)\left(x+y-8\right)=0\left\{x^{2}+\left(y-8\right)^{2}>5\ \right\}\left\{\left(x-3\right)^{2}+\left(y-3\right)^{2}>4\right\}\left\{4<y<8\right\}
\left(x-2\right)^{2}+\left(y+6\right)^{2}=0.25
\left(x-7\right)^{2}+\left(y+2\right)^{2}=0.25
x^{2}+\left(y-8\right)^{2}=0.25
x=0\left\{8.5<y<12\right\}
\left(x+6\right)^{2}+\left(y+9\right)^{2}=0.25
\left(x-3\right)^{2}+\left(y+4\right)^{2}=0.25
\left[\left(-6,5\right),\left(-5,3\right),\left(-7,3\right),\left(-3,1\right),\left(-3,-1\right),\left(0,-1\right),\left(1,-3\right),\left(-1,-3\right),\left(1,-7\right),\left(-1,-7\right),\left(0,-6\right),\left(0,-8\right),\left(6,-3\right),\left(7,-5\right),\left(5,-5\right),\left(6,6\right),\left(7,4\right),\left(8,3\right)\right]
x^{2}+y^{2}=144
x^{2}+y^{2}=160

I couldn't fix it

Latex won't show normally if it's really long.

Last edited by Temporary username (2022-11-02 18:18:13)

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#154 2022-11-02 21:20:11

Bob
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Registered: 2010-06-20
Posts: 9,607

Re: LaTeX - A Crash Course

hi Temporary username

Welcome to the forum.

I think the poster didn't intend the LaTex to show here; but rather on the Dr Who site given.

Years ago MIF-Forum used a different server but had to change.  Some LaTex that worked on the orignal now fails because the commands aren't implemented now. Cannot do a lot about it I'm afraid sad

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#155 2022-11-04 02:46:52

ganesh
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Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

A quadratic equation solution is

or

x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}
x = (-b \pm \sqrt(b^2 - 4ac))/(2a).

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#156 2022-11-04 17:11:56

ganesh
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Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Square, cube, and nth power; square root, cube root and nth root

a^2

gives

a^3

gives

a^n

gives

\sqrt{n}

gives

\sqrt[3]{n}

gives

\sqrt[a]{n}

gives

For example,

\sqrt[6]{64}

gives

which is 2.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#157 2022-11-05 01:22:53

ganesh
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Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Some Algebraic Expansions

(a + b)^2 = a^2 + 2ab + b^2

gives

(a - b)^2 = a^2 - 2ab + b^2

gives

(a + b)^3 = a^3 + 3a^2b + 3ab^3 + b^3

gives

(a - b)^3 = a^3 - 3a^3 + 3ab^2 - b^3

gives

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

gives

a^3 - b^3  = (a - b)(a^2 + ab + b^2

gives

.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#158 2022-11-05 21:40:10

ganesh
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Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Factorial, Permutations, and Combinations

n! = n \times (n - 1) \times (n - 2) \times .... 3 \times 2 \times 1 = n!

gives

nP_r = \dfrac{n!}{(n - r)!}

gives

nC_r = \dfrac{n!}{(n - r)!r!}

gives

.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#159 2022-11-06 02:39:18

ganesh
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Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Summation

\Sigma \ n = \dfrac{n(n+ 1)}{2}

gives

\Sigma \ n^2 = \dfrac{n(n + 1)(2n + 1)}{6}

gives

\Sigma \ n^3 = \left[\dfrac{n(n +1)}{2}\right]^2

gives


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#160 2022-11-06 15:49:22

ganesh
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Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Arithmetic Progression

nth term of a Arithmetic Progression is

a_n = a + (n - 1)d

given by

where a is the first term, n is the number of terms, d is the common difference, and

is the nth term.

Sum of n terms of an Arithmetic Progression :

S_n = n/2[2a + (n - 1)d]

is

.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#161 2022-11-06 20:53:59

ganesh
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Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Geometric Progression

nth term is

a_n = ar^{n - 1}

gives

Sum of the terms

\Sigma = a\left(\dfrac{1 - r^n}{1 - r}\right)

gives

or

\Sigma = a\left(\dfrac{r^n - 1}{r - 1}\right)

gives

.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#162 2022-11-11 20:03:42

ganesh
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Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Circle, Hemisphere, and Sphere

Area of a Circle:

\pi{r^2}

written as

is the Area of a circle.

2\pi{r}

written as

is the Circumference of a circle.

\dfrac{2}{3}

written as

is the Volume of a Hemisphere.

\dfrac{4}{3}\pi{r^3}

written as

is the Volume of a Sphere.

{3}\pi{r^2}

written as

is the Surface area of a Hemisphere.

4\pi{r^2}

written as

is the Surface area of a sphere.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#163 2022-11-12 21:23:30

ganesh
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Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Two Dimensions

Rectangle :

lb

is

Square:

a^2

is

Triangle:

\dfrac{1}{2}bh

is

where b is base and h is height.

Hero's formula for Area of a Triangle:

\sqrt{s(s - a)(s - b)(s - c)}

is

where a, b, and c are side lengths and s is semi-perimeter (half of perimeter).


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#164 2022-11-13 15:41:32

ganesh
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Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Parallelogram, Trapezium, Kite, and Quadrilateral

Area of a Parallelogram:

Area = Base \times Height

is

where b is the base and h is the height.

Perimeter:

P = 2(a + b)

is

where a and b are the two sides of a Parallelogram.

Area of Rhombus:

Area = \dfrac{d_1 \times d_2}{2}

is

where d1 and d2 are length of diagonals.

Perimeter:

4a

is

.

Kite:

Area = \dfrac{pq}{2}

is

where p and q are the diagonals.

Perimeter :

Perimeter: 2 x (sum of lengths of the sides)

is

Trapezium:

Area = \dfrac{a + b}{2}h

is

where a, b are sides and h is the height.

Quadrilateral:

Area: 1/2 x diagonal x (sum of perpendicular heights)

is

Perimeter: a + b + c + d

is

.

Perimeter: sum of lengths sides of the quadrilateral.

is


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#165 2022-11-16 18:11:04

ganesh
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Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Cylinder and Cone

Right Circular Cylinder

Volume:

\pi{r^2}h

gives

.

Surface Area:

2\pr{r}h

gives

where r is radius, h is height.

Right Circular Cone

Volume:

\dfrac{1}{3}\pi{r^2}h

gives

.

Area:

\pi{r}(r + l)

gives

where l is slant height.

Slant height:

\sqrt(r^2 + h^2)

gives

.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#166 2022-11-17 17:14:16

ganesh
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Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Hollow Sphere, Hollow Right Cylinder, Hollow Right Circular Cone

Volume

Sphere = \dfrac{4}{3}\pi(R^3 - r^3)

gives

where R and r are external and internal radii.

Right Circular Cylinder = \pi({R^2 - r^2})h

gives

.

Right Circular Cone = \dfrac{1}{3}\pi(R^2 - r^2)h

gives


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#167 2022-11-17 21:38:31

ganesh
Administrator
Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Exponents

a^m \times a^2 = a^{m + n}

gives

\dfrac{a^m}{a^n} = a^{m - n}

gives

(a^m)^{n}) = a^{mn}

gives

a^0 = 1, a \neq 0

gives

.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#168 2022-11-18 17:43:55

ganesh
Administrator
Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Rational Numbers

\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd}

gives

\dfrac{a}{b} - \dfrac{c}{d} = \dfrac{ad - bc}{bd}

gibes

\frac{a}{b} \times \dfrac{c}{d} = \dfrac{ac}{bd}

gives

\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{ad}{bc}

gives

.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#169 2022-11-19 02:24:12

ganesh
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Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Quadratic Equation

Standard form : ax^2 + bx + c = 0

gives

.

Forming a Quadratic Equation:

We will learn the formation of the quadratic equation whose roots are given.

To form a quadratic equation, let

\alpha and \beta

is

and
be the two roots.

Let us assume that the required equation be

ax^2  + bx + c = 0, a \neq 0

is

According to the problem, roots of this equation are

\alpha and \beta

gives

and
.

Therefore,

\alpha + \beta = -\dfrac{b}{a} and \alpha\beta = \dfrac{c}{a}

gives

and

Now,

ax^2 + bx + c = 0

gives

x^2 + \dfrac{b}{a}x + \dfrac{c}{a}a = 0 (Since, a \neq 0)

gives

.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#170 2022-11-20 17:22:23

ganesh
Administrator
Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Surface Area

Sphere:

Curved surface area (CSA) :

The Curved surface area of hollow sphere is the area of the paper that can completely cover the surface of the hollow sphere. It is equal to the CSA of inner sphere subtracted from the CSA of outer sphere.

CSA of hollow sphere, = CSA of outer sphere - CSA of inner sphere

= 4\pi(R^2) - 4\pi(r^2)

is

= 4 \pi(R^2-r^2)

is

.

Total surface area of hollow sphere :

The total surface area of a hollow sphere is equal to the CSA of hollow sphere as a hollow sphere has only one surface that constitutes it.

Thus CSA=TSA for a hollow sphere


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#171 2022-11-20 18:46:27

ganesh
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Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Surface Area

Cylinder:

Total:

Area = 2\pi{r^2} + 2\pi{r}h

gives

where r is radius, h is the height.

Curved Surface Area:

Area = 2\pi{r}h

gives

.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#172 2022-11-20 19:17:58

ganesh
Administrator
Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Cone

Surface Area

The surface area of a cone is equal to the curved surface area plus the area of the base:

\pi{r^2} + \pi{l}r

gives

, where r denotes the radius of the base of the cone, and L denotes the slant height of the cone. The curved surface area is also called the lateral area.

l = \sqrt{r^2 + h^2}

gives

where r is radius and h height.

Curved Surface Area:

Area = \pi{r}l

gives

l


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#173 2022-11-21 17:26:59

ganesh
Administrator
Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Set Formulas

If A, B, and C are three sets, then the number of elements

n(A \cup B) = n(A) + n(B) - n(A \cap B)

gives

.

If

A \cap B = \phi, then n(A \cup B) = n(A) + n(B)

gives

n(A \cup B \cup C) = n(A) + n(B) + n(C) - n(A \cap B) - n(B \cap C) - n(C \cap A) + n(A \cap B \cap C)

gives

.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#174 2022-11-22 01:08:49

ganesh
Administrator
Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Simple Interest

Simple Interest = Prt where P is Principal, r is rate of Interest, and t time (months, quarters, years etc.)

gives

,

Compound Interest

Compound Interest

gives

A = P\left(1 + \dfrac{r}{n}\right)^{nt}

gives

where:

* A is the final amount
* P is the original principal sum
* r is the nominal annual interest rate
* n is the compounding frequency
* t is the overall length of time the interest is applied (expressed using the same time units as r, usually years).


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#175 2022-11-22 20:38:51

ganesh
Administrator
Registered: 2005-06-28
Posts: 40,453

Re: LaTeX - A Crash Course

Profit and Loss

Profit = Selling Price - Cost Price

gives

Loss = Cost Price - Selling Price

gives

Profit Percentage = \dfrac{Profit}{Cost \ Price} \ times \ 100\%

gives

Loss Percentage = \dfrac{Loss}{Cost \ Price} \times 100\%

gives


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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