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OpenMath

Palettes

Linear Line (Single)

plot(2 · x + 3, x = -10..10)

2D straight line with slope and y-intercept

Multiple Lines

plot([2 · x + 1, -x + 4, 0.5 · x - 2], x = -5..5)

Compare multiple linear curves on the same plot

Quadratic / Parabola

plot(x² - 4 · x + 3, x = -2..6)

Parabola with vertex and roots

Cubic Polynomial

plot(x³ - 3 · x, x = -2.5..2.5)

3rd degree polynomial curve

Sine Wave

plot(sin(x), x = -2 · π .. 2 · π)

Periodic harmonic sine wave

Cosine Wave

plot(cos(x), x = -2 · π .. 2 · π)

Periodic harmonic cosine wave

Damped Oscillation

plot(exp(-0.2 · x) · cos(2 · x), x = 0..20)

Decaying sinusoidal oscillation curve

Exponential Decay

plot(exp(-x/2), x = 0..10)

Exponential decay function

Rational Curve

plot(1 / (x² + 1), x = -5..5)

Bell-shaped rational curve

Parametric Circle

plot([cos(t), sin(t)], t = 0 .. 2 · π)

2D parametric circular trajectory

Polar Rose

plot(cos(4 · theta), theta = 0 .. 2 · π)

4-petal polar rose plot

Feasible Region (LP)

polygonOmråde([x >= 0, y >= 0, x + y <= 10], x = 0..12, y = 0..12)

Linear programming feasible polygon

LP Level Curves

LPplot(30 · x + 20 · y, [x >= 0, y >= 0, x + y <= 10], [100, 200, 300])

Optimization objective level lines

3D Surface Plot

plot3d(sin(x) · cos(y), x = -π .. π, y = -π .. π)

3D bivariate surface plot

Ohm's Law

V := I · R

Voltage, current, and resistance: V = I · R

Voltage Divider

voltage_divider(5.0, 10000, 4700)

Calculate Vout from Vin, R1, and R2

Parallel Resistors

R_eq := (R_1 · R_2) / (R_1 + R_2)

Equivalent resistance of parallel pair

RC Low-Pass Cutoff

rc_cutoff(10 · kOhm, 100 · nF)

fc = 1 / (2 · π · R · C)

RC Time Constant

tau := R · C

Step response time constant tau = R · C

ADC Voltage to Count

adc_volt(3.3, 3.3, 12)

Convert analog volts to N-bit digital integer

ADC Count to Voltage

adc_raw(2048, 3.3, 12)

Convert raw digital count to measured volts

UART Baud Divisor

ubrr_calc(72 · MHz, 115200)

Calculate UART clock prescaler register

Timer ARR Prescaler

timer_calc(72 · MHz, 1000)

Timer auto-reload & prescaler for frequency

Bit Set

bit_set(0x00, 3)

Set bit n in register: reg | (1 << bit)

Bit Clear

bit_clear(0xFF, 3)

Clear bit n in register: reg & ~(1 << bit)

Bit Toggle

bit_toggle(0x00, 2)

Toggle bit n in register: reg ^ (1 << bit)

Extract Bitfield

bit_field(0xABCD, 4, 8)

Extract bits at given offset and width

Binary Representation

to_bin(0xA5, 8)

Format integer as binary bit string

Hex Representation

to_hex(165, 8)

Format integer as hexadecimal string

Two's Complement

two_comp_repr(-42, 8)

Signed 2's complement representation

Electric Power (P = I²R)

P := I² · R

Electrical power dissipated in resistor

Capacitor Energy

E := (1/2) · C · V²

Stored electrical energy in joules

Inductive Reactance (XL)

XL := 2 · π · f · L

AC impedance of inductor in ohms

Capacitive Reactance (XC)

XC := 1 / (2 · π · f · C)

AC impedance of capacitor in ohms

Derivative

diff(f(x), x)

Differentiate f(x) with respect to x

Definite Integral

integrate(f(x), (x, a, b))

Definite Riemann integral from a to b

Indefinite Integral

integrate(f(x), x)

Antiderivative of f(x)

Summation

Sum(k², (k, 1, n))

Sum of terms from k=1 to n

Product

Product(k, (k, 1, n))

Product of terms from k=1 to n

Square Root

sqrt(x² + 1)

Square root radical

Base-10 Logarithm

log(x, 10)

Common logarithm base 10

Solve Equation

solve(f(x) = 0, x)

Solve algebraic equation for x

Solve System

solve([x + y = 10, 2 · x - y = 4], [x, y])

Solve system of simultaneous equations

Taylor Series

taylor(f(x), x, 0, 5)

Taylor polynomial expansion

Limit

limit(f(x), x, 0)

Evaluate limit as x approaches value

Name	Value
No user variables defined.

Evaluate:	Enter
Evaluate Inline:	Alt+Enter
Toggle Math/Text:	F5
Exit Fraction/Power:	→
Assignments:	a := b
Functions:	f := x -> x²
Equations:	x = y
Navigate Tabs:	Tab

Evaluate active group:	Enter
Execute entire worksheet:	Ctrl+Shift+Enter
Toggle 2D Math / Text:	F5
New Worksheet:	Ctrl+N
Open Document:	Ctrl+O
Save Document:	Ctrl+S
Matrix Wizard:	Ctrl+M
Insert cell after:	Ctrl+J
Insert cell before:	Ctrl+K
Zoom In / Out:	Ctrl++ / Ctrl+-

OpenMath

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