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waht
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Introduction:
WolframAlpha is a freely available computational engine that can supplement already existing software such as mathematica, maple, mathlab, or excel. The purpose of this mini-guide is to go over some of its functionality with emphasis on electrical engineering.
www.wolframalpha.com
Dimensional analysis:
WolframAlpha recognizes many common units. It will simplify dimensions and scale units. For example,
will generate [time]^2
will generate 10,000 pF or 10 nF
WolframAlpha also can tap its database to pull up a conversion formula from the context
will convert the frequency to wavelength 12 meters
will give energy in a capacitor,
or to find inductance to resonate with 10 nF capacitor at 100 Khz; just say that
output 253 nH
Also if you haven't memorized resistor color bands already, you can still look them up
output: 4.7KComplex numbers and phasors:
Working in polar form is supported in W|A. By typing an impedance in rectangular form
we are quickly given its magnitude and phase of 54, and 56 degrees
and likewise, we can indicate a phasor in polar form with an exponential e
generates -1
we can also manipulate phasors algebraically
output: magnitude = 124, phase = 42 deg
indicate degrees with “deg” otherwise W|A will interpret it in radians.Solving equations:
To solve x^2 - 2x + 1= 0, enter the equation as it is
output x = 1
and W|A solves it. Don't even have to specify the variable to be solved.
Solving systems of equations is just as easy,
v_1 + v_2 + v_3 = 4
v_1 - v_2 = 10
v_1 - 3v_2 + 5v_3 = 8
simply type
output v1 = 23/3, v2 = -7/3, v3 = -4/3
just make sure that the equations are separated by a comma.
Differential equations are supported as well. An nth number of apostrophes indicates an nth derivative, and proceed as before. For example to solve
\frac{d^2y}{dx^2} - \frac{dy}{dx} - 2y = 0 \indent y(0) = 1, y'(0) = 2
enter the code as follows,
and we get a solution y = e^2x as well as a plot that can be saved in pdf format, and printed out.We can also maximize and minimize
finds maximum of 1Logic gates and boolean algebra:
Converts number bases,
= 7d
We can also work with boolean expression in WolramAlpha, for example
generates a truth table:http://img200.imageshack.us/img200/9384/truthtable.gif
a schematic with logic gates, and even simplifies the expression to a minimal form
http://img268.imageshack.us/img268/3233/scehmatic.gif
Here is the supported syntax:
More on calculus:
W|A can perform basic calculus
take derivatives:
\frac{d}{dt} cos(t)
do integration:
\int \frac{1}{x+1} dx
and take Laplace and Fourier transforms:
\mathcal{L}(x^2), \mathcal{F}(e^x)
Plotting:
If you want to graph a transfer function for instance,
H(s) = \frac{s+10}{s^2 + 4s + 8}
enter:
and here we have
http://img32.imageshack.us/img32/9715/graph.gif Conclusion:
WolframAlpha uniquely combines different tools into a one freely available package and that expands our tool box. This mini-guide doesn't cover all of W|A, it merely touches upon features that can be used in electrical engineering, for more information visit their examples page
http://www28.wolframalpha.com/examples/
also, W|A is said to expand in the future, enabling more functionality, and tools.
WolframAlpha is a freely available computational engine that can supplement already existing software such as mathematica, maple, mathlab, or excel. The purpose of this mini-guide is to go over some of its functionality with emphasis on electrical engineering.
www.wolframalpha.com
Dimensional analysis:
WolframAlpha recognizes many common units. It will simplify dimensions and scale units. For example,
Code:
farad * henry
Code:
0.01 uF to pFWolframAlpha also can tap its database to pull up a conversion formula from the context
Code:
convert 25 MHz to meters
Code:
find energy in 100 uF at 10 KVor to find inductance to resonate with 10 nF capacitor at 100 Khz; just say that
Code:
find inductance for 10 nF at 100 KHzAlso if you haven't memorized resistor color bands already, you can still look them up
Code:
resistor yellow purple redoutput: 4.7KComplex numbers and phasors:
Working in polar form is supported in W|A. By typing an impedance in rectangular form
Code:
30 + 45iand likewise, we can indicate a phasor in polar form with an exponential e
Code:
e^(i pi)we can also manipulate phasors algebraically
Code:
100 e^(i 45 deg) + 25 e^(i 30 deg)indicate degrees with “deg” otherwise W|A will interpret it in radians.Solving equations:
To solve x^2 - 2x + 1= 0, enter the equation as it is
Code:
x^2 - 2x + 1 = 0and W|A solves it. Don't even have to specify the variable to be solved.
Solving systems of equations is just as easy,
v_1 + v_2 + v_3 = 4
v_1 - v_2 = 10
v_1 - 3v_2 + 5v_3 = 8
simply type
Code:
v1 + v2 + v3 = 4, v1-v2 = 10, v1 - 3v2 + 5v3 = 8just make sure that the equations are separated by a comma.
Differential equations are supported as well. An nth number of apostrophes indicates an nth derivative, and proceed as before. For example to solve
\frac{d^2y}{dx^2} - \frac{dy}{dx} - 2y = 0 \indent y(0) = 1, y'(0) = 2
enter the code as follows,
Code:
y'' – y' - 2 y = 0, y(0) = 1, y'(0) = 2
Code:
max 1 - x^2Converts number bases,
Code:
binary 1111101 to hexWe can also work with boolean expression in WolramAlpha, for example
Code:
(x or y) and (x or !y)a schematic with logic gates, and even simplifies the expression to a minimal form
http://img268.imageshack.us/img268/3233/scehmatic.gif
Here is the supported syntax:
Code:
NOT = !
OR = ||
AND = &&
NAND
NOR
XORW|A can perform basic calculus
take derivatives:
\frac{d}{dt} cos(t)
Code:
derivative cos(t)do integration:
\int \frac{1}{x+1} dx
Code:
integrate 1/(x+1) dxand take Laplace and Fourier transforms:
\mathcal{L}(x^2), \mathcal{F}(e^x)
Code:
laplace x^2
Code:
fourier e^xIf you want to graph a transfer function for instance,
H(s) = \frac{s+10}{s^2 + 4s + 8}
enter:
Code:
graph (s + 10)/(s^2 + 4s + 8)and here we have
http://img32.imageshack.us/img32/9715/graph.gif Conclusion:
WolframAlpha uniquely combines different tools into a one freely available package and that expands our tool box. This mini-guide doesn't cover all of W|A, it merely touches upon features that can be used in electrical engineering, for more information visit their examples page
http://www28.wolframalpha.com/examples/
also, W|A is said to expand in the future, enabling more functionality, and tools.
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