# Manual

**If you start this program the first time check out the getting started manual.**

**Calculator:** Expressions are evaluated as you type. To add a new line of calculations press `OK`

. Scroll up to see the previous calculations. To switch between radians and degrees, press the options button at the top of the keyboard. The `NaN`

answer means "not a number". Press ‘Ans’ to get last answer. Note: the last answer must be a number, e.g. the result of a differentiation won’t change the value of ‘Ans’.

If you press `^`

or `/`

you will see that Algeo intelligently places the exponent and the denominator. For example pressing `2`

then `^`

makes the cursor jump to the exponent level. Here you can enter the exponent. When you want jump down to the normal level simply tap to the right of the expression on a blank field. You can also use the arrow keys to move the cursor..

**Using variables:** There are four variables:`a`

, `b`

, `d`

and `t`

(the letter `c`

is reserved for the speed of light constant). You can enter them by long pressing the corresponding number. The default value for the variables is 0. To set their values use ‘=’. Example:

`a=2+1`

`a^2`

→ `9`

**Constants:** There are several predefined physical constants under the CONST button. They include mathematical constants, such as *e* or π and other numbers, like the speed of light or gravity.

**Using graphs:** You can move the graph by touch. To zoom in and out, use the buttons in the lower right corner. You can trace the function by choosing the Trace icon from the upper bar. On every plot line a dot appears. Move your finger across the screen to move the dots. It snaps automatically to intersections and roots of functions. In the upper part of the screen you will see the values of the graphed functions evaluated where the dot is.

It is possible to draw polar-coordinate plots, instead of regular Cartesian functions. To use polar-coordinates, in the Graph input screen tap ‘Cartesian’ in the top right corner to flip it to polar-coordinate mode. Here, instead of `y`

, the changing variable is `θ`

.

**Table of values:** You can generate a numeric table of the functions you specified in the Graph Menu. Simply press the button Table. The display shows a list with the values of the functions at the given intervals. You can modify the range settings by pressing the "Settings" icon on the top bar. Pressing "Reset Range" sets the range to the interval `[1;10]`

.

## Advanced functions

**Solving equations:** The `solve`

function will solve the given expression in `x`

. If there is no `=`

sign in the equation then it will be solved for 0. So in the example below it solves the equation `x^2=0`

. It only finds one solution. Examples:

`solve(x^2)`

→ `0`

`solve(sinx=cosx)`

→ `0.785398`

**Differentiation:** You can differentiate with the `diff`

function. Its sole parameter is the expression to differentiate. Examples:

`diff(x^2)`

→ `2*x`

`diff(tg(x))`

→ `cos(x)^(-2)`

`diff(diff(sin(x)))`

→ `-sin(x)`

**Integration:** Use the `int`

function to calculate the definite integral of a function. The first parameter is the function to integrate, the other two are the limits of the integral. Examples:

`int(x,0,10)`

→ `50`

`int(sinx,-1,1)`

→ `0`

**Taylor-series:** To calculate the Taylor-series of a function use the `taylor`

function. The first parameter is the function, the second is the point the Taylor-series is centered, and third one is the exponent of the biggest element. Examples:

`taylor(ln(x),1,3)`

→ ` x-1-(x-1)^2/2!+(x-1)^3/3!`

`taylor(sinx,0,4)`

→ `-x^3/3!`

**Combinatorics:** The two combinatorial functions, `nPr`

and `nCr`

lets you calculate permutations and combinations. `nPr`

calculates the number of r-permutations of n. It gives the the number of ways you can choose r elements and put them in a row from n elements. `nCr`

calculates the number of r-combinations of a set with n elements. It gives the the number of ways you can choose r elements from n elements. Examples:

`nPr(5,2)`

→ `20`

`nCr(5,3)`

→ `10`

**Other functions:** The functions not explained above are listed in the following table:

Function | Description | Example |
---|---|---|

abs | Absolute value | `abs(-5)` → `5` |

exp | Exponential function | `exp(1)` → `2.7182` |

frac | Fractional part | `frac(1.34)` → `0.34` |

floor | Floor function, the integer part | `floor(1.34)` → `1` |

gcd | Greatest common divisor | `gcd(6,4)` → `2` |

log | 10-based logarithm | `log(100)` → `2` |

mod | Calculating remainder | `mod(11,4)` → `3` |