NASA will launch an expedition to Mars in July 2020. The spacecraft will deliver to Mars an electronic carrier with the names of all registered members of the expedition.

Registration of participants is open. Get your Mars ticket from this link.

If this post solved your problem or you just liked it, share the link to it with your friends on social networks.

One of these code variants must be copied and pasted into the code of your web page, preferably between the tags and or right after the tag ... According to the first option, MathJax loads faster and slows down the page less. But the second option automatically tracks and loads the latest versions of MathJax. If you insert the first code, then it will need to be updated periodically. If you insert the second code, the pages will load more slowly, but you will not need to constantly monitor MathJax updates.

The easiest way to connect MathJax is in Blogger or WordPress: in your site's dashboard, add a widget for inserting third-party JavaScript code, copy the first or second version of the loading code presented above into it, and place the widget closer to the beginning of the template (by the way, this is not necessary at all because the MathJax script is loaded asynchronously). That's all. Now, learn the MathML, LaTeX, and ASCIIMathML markup syntax, and you're ready to embed math formulas into your website's web pages.

Another New Year's Eve ... frosty weather and snowflakes on the window pane ... All this prompted me to write again about ... fractals, and what Wolfram Alpha knows about it. There is an interesting article about this, which contains examples of two-dimensional fractal structures. Here we will look at more complex examples of 3D fractals.

A fractal can be visualized (described) as a geometric figure or body (meaning that both are a set, in this case, a set of points), the details of which have the same shape as the original figure itself. That is, it is a self-similar structure, considering the details of which with magnification, we will see the same shape as without magnification. Whereas in the case of a regular geometric shape (not a fractal), when we zoom in, we will see details that have a simpler shape than the original shape itself. For example, at a high enough magnification, part of the ellipse looks like a line segment. This does not happen with fractals: at any increase in them, we will again see the same complex shape, which will repeat over and over again with each increase.

Benoit Mandelbrot, the founder of the science of fractals, wrote in his article Fractals and Art for Science: “Fractals are geometric shapes that are as complex in their details as in their general form. part of the fractal will be enlarged to the size of the whole, it will look like a whole, or exactly, or perhaps with a slight deformation. "

Integration is an important tool in calculus that can give an antiderivative or represent area under a curve.

The indefinite integral of `f (x)`, denoted `int f (x) \ dx`, is defined to be the antiderivative of` f (x) `. In other words, the derivative of `int f (x) \ dx` is` f (x) `. Since the derivative of a constant is zero, indefinite integrals are defined only up to an arbitrary constant. For example, `int sin (x) \ dx = -cos (x) +" constant "`, since the derivative of `-cos (x) +" constant "` is `sin (x)`. The definite integral of `f (x)` from `x = a` to` x = b`, denoted `int_ (a) ^ (b) f (x) \ dx`, is defined to be the signed area between` f (x) `and the` x` axis, from `x = a` and` x = b`.

Both types of integrals are tied together by the fundamental theorem of calculus. This states that if `f (x)` is continuous on `` and `F (x)` is its continuous indefinite integral, then `int_ (a) ^ (b) f (x) \ dx = F (b) - F (a)`... This means `int_ (0) ^ (pi) sin (x) \ dx = (-cos (pi)) - (- cos (0)) = 2`... Sometimes an approximation to a definite integral is desired. A common way to do so is to place thin rectangles under the curve and add the signed areas together. Wolfram | Alpha can solve a broad range of integrals.

How Wolfram | Alpha calculates integrals

Wolfram | Alpha computes integrals differently than people. It calls Mathematica "s Integrate function, which represents a huge amount of mathematical and computational research. Integrate doesn" t do integrals the way people do. Instead, it uses powerful, general algorithms that often involve very sophisticated math. There are a couple of approaches that it most commonly takes. One involves working out the general form for an integral, then differentiating this form and solving equations to match undetermined symbolic parameters. Even for quite simple integrands, the equations generated in this way can be highly complex and require Mathematica "s strong algebraic computation capabilities to solve. Another approach that Mathematica uses in working out integrals is to convert them to generalized hypergeometric functions, then use collections of relations about these highly general mathematical functions.

While these powerful algorithms give Wolfram | Alpha the ability to compute integrals very quickly and handle a wide array of special functions, understanding how a human would integrate is important too. As a result, Wolfram | Alpha also has algorithms to perform integrations step by step. These use completely different integration techniques that mimic the way humans would approach an integral. This includes integration by substitution, integration by parts, trigonometric substitution, and integration by partial fractions.

An online mathematical processor, a knowledge processor that, at your request, provides data about the world around you in numbers.

It all looks very simple - you enter your query in the search field, press the "=" button, you get the result:

In fact, WolframAlpha provides free and unlimited access to its knowledge base, which includes a huge amount of information about our world in numerical terms. Demography, economics, history, linguistics, physics, biology, chemistry ..., and of course MATHEMATICS - mathematical rules, formulas, algorithms - there is all this, and much, much more.

For math students, WolframAlpha is a godsend. This web service easily solves equations and systems, plots functions, calculates limits, finds derivatives, takes integrals ...

It looks like it's hard to find a problem that WolframAlpha can't handle. You just need to correctly formulate your request. By the way, although WolframAlpha uses a special syntax, as in other systems of computer mathematics, however, it understands quite well the usual questions asked in ordinary English. For example, you might ask WolframAlpha: “How many students are in Russia now?” Are you wondering what WolframAlpha will answer?

How do I use WolframAlpha? A brief description of the service capabilities in Russian is available.

To get to know WolframAlpha in detail, and learn more about how to use this service for mathematical calculations, it is worth looking at the only web resource where the mathematical capabilities of WolframAlpha are detailed, accessible and systematically described in Russian - this is the Wolfram | Alpha blog in Russian.

This blog is still the only one of this kind, probably also because a competent and complete description of the mathematical capabilities of WolframAlpha is a rather difficult task for students (enthusiasts or moneymakers) (even very good ones!), Who usually take the trouble to host and maintain mathematical resources in Runet. What's more, WolframAlpha's math skills, which start at the most rudimentary, extend too far beyond the standard university math course. I think they can be compared without a stretch to the mathematical abilities of Stephen Wolfram himself, the developer of the Mathematica system and the mastermind of WolframAlpha.

These abilities are partly illustrated by examples of solving problems from different areas of mathematics posted on the service support site.

Take a look at how WolframAlpha solves a system of two nonlinear algebraic equations of equations x ^ 2-2y + 1 = 0, x ^ 3 + y ^ 2 = 6:

Since the WolframAlpha math engine works on the basis of algorithms from the well-known computer mathematics system Mathametica, these results can be completely trusted.

The knowledge base from which WolframAlpha draws its abilities is constantly updated with relevant materials, factual and numerical data, algorithms - every day WolframAlpha is becoming "smarter"! The capabilities of this system best allow you to evaluate numerous examples of its use from different fields of knowledge.

Among other things, WolframAlpha offers a variety of math products: free widgets for websites, inexpensive mobile math apps for installing on students' smartphones, add-ons and plugins for major browsers, developer tools and so on.

For example, for ease of use, you can embed a Wolfram Alpha query box on your site. But if you have already appreciated the capabilities of Wolfram Alpha, then for sure you want to have this tool always at hand. It is enough to install in your browser a suitable extension, toolbar or plug-in from among those offered by the official Wolfram Alpha website. With them, you can turn to Wolfram Alpha at any time. More on this.

Recently, WolframAlpha has started using a new math document format - CDF. It is a format that allows you to create documents containing interactive math objects. For example, these can be graphs of functions, differential equations, and the like. The user can change the parameters of such objects using the controls built into the document, while simultaneously observing the changes taking place (similar to the GeoGebra Java applets). Based on this format, as well as the Wolfram Alpha widgets, you can, for example, create dynamic illustrations of mathematical rules and algorithms, conduct research, and laboratory classes in mathematics.

Get to know Wolfram Alpha immediately if you haven't already!

+	addition
-	subtraction
*	multiplication
/	division
^	exponentiation
solve	solution of equations, inequalities, systems of equations and inequalities
expand	opening brackets
factor	factorization
sum	calculating the sum of the members of a sequence
derivative	differentiation (derivative)
integrate	integral
lim	limit
inf	Infinity
plot	plot a function
log ( a, b)	logarithm to base a the numbers b
sin, cos, tg, ctg	sine, cosine, tangent, cotangent
sqrt	square root
pi	pi (3.1415926535 ...)
e	number "e" (2.718281 ...)
i	Imaginary unit i
minimize, maximize	Finding extrema of a function (minimums and maximums)

Examples of online problem solving with WolframAlpha

1. Solution of rational, fractional-rational equations of any degree, exponential, logarithmic, trigonometric equations.
Example 1 ... To solve the equationx 2 + 3 x- 4 = 0, you need to entersolve x ^ 2 + 3x-4 = 0
Example2. To solve the equation log 3 2 x = 2 , you need to enter solve log (3, 2x) = 2
Example3. To solve equation 25 x-1 = 0.2, you need to enter solve 25 ^ (x-1) = 0.2
Example4. To solve the equation sin x = 0.5, you need to enter solve sin (x) = 0.5

2. Solution of systems of equations.
Example... To solve the system of equations

x + y= 5,
x - y = 1,

need to enter solve x + y = 5&& x-y = 1
Signs &&

3. Solution of rational inequalities of any degree.
Example... To solve the inequalityx 2 + 3 x - 4 < 0, нужно ввести solve x ^ 2 + 3x-4<0

4. Solution of systems of rational inequalities.
Example. To solve the system of inequalities

x 2 + 3 x - 4 < 0,
2 x 2 - x + 8 > 0,

need to enter solve x ^ 2 + 3x-4<0 && 2x ^ 2- x + 8 > 0
Signs && in this case denotes a logical "AND".

5. Expansion of brackets + casting of similar ones in the expression.
Example ... To expand the parentheses in the expression ( c + d) 2 (a-c) and bring similar ones, you need
enter expand (c + d) ^ 2 * (a-c).

6. Factoring the expression.
Example ... To factor the expressionx 2 + 3 x- 4, you need to enter factor x ^ 2 + 3x - 4.

7. Calculation of the amount n the first members of the sequence (including arithmetic and geometric progressions).
Example ... To calculate the sum of the first 20 terms of the sequence given by the formula a n = n 3 +n, you need to enter sum n ^ 3 + n, n = 1..20
If you need to calculate the sum of the first 10 members arithmetic progression with the first terma 1 = 3, difference d a1 = 3, d = 5, sum a1 + d (n-1), n ​​= 1..10
If you need to calculate the sum of the first 7 members geometric progression with the first termb 1 = 3, difference q= 5, then you can, as an option, enter b1 = 3, q ​​= 5, sum b1 * q ^ (n-1), n ​​= 1..7

8. Finding derivative.
Example ... To find the derivative of a function f(x) = x 2 + 3 x- 4, you need to enter derivative x ^ 2 + 3x - 4

9. Finding definition of the indefinite integral.
Example ... To find the antiderivative of a function f(x) = x 2 + 3 x- 4, you need to enter integratex ^ 2 + 3x - 4

10. Calculation definite integral.
Example ... To calculate the integral function f(x) = x 2 + 3 x- 4 on the segment,
need to enterintegratex ^ 2 + 3x - 4, x = 5..7

11. Calculation limits.
Example ... To make sure that

enter lim (x -> 0) (sin x) / x and see the answer. If you need to calculate some limit at x tending to infinity, one should introduce x -> inf.

12. Research function and plotting .
Example ... To investigate the functionx 3 - 3 x 2 and plot it, just enter x ^ 3-3x ^ 2. You will get the roots (the points of intersection with the axis OH), derivative, graph, indefinite integral, extrema.

13. Finding the largest and smallest values ​​of a function on a segment .
Example ... To find minimal function valuex 3 - 3 x 2 on the segment,
need to enter minimize (x ^ 3-x ^ 2), (x, 0.5, 2)
To find the maximum function valuex 3 - 3 x 2 on the segment,
need to enter maximize (x ^ 3-x ^ 2), (x, 0.5, 2)

1. Solution of rational, fractional-rational equations of any degree, exponential, logarithmic, trigonometric equations.

Example 1. To solve the equation x 2 + 3x- 4 = 0, you need to enter solve x ^ 2 + 3x-4 = 0

Example 2. To solve the equation log 3 2 x= 2, you need to enter solve log (3, 2x) = 2

Example 3. To solve equation 25 x-1 = 0.2, you need to enter solve 25 ^ (x-1) = 0.2

Example 4. To solve the equation sin x= 0.5, you need to enter solve sin (x) = 0.5

2. Solution of systems of equations.

Example... To solve the system of equations

x + y= 5,

x — y = 1,

you need to enter solve x + y = 5 && x-y = 1

Signs &&

3. Solution of rational inequalities of any degree.

Example... To solve the inequality x 2 + 3x — 4 < 0, нужно ввести solve x^2+3x-4<0

4. Solution of systems of rational inequalities.

Example. To solve the system of inequalities

x 2 + 3x — 4 < 0,

2x 2 — x + 8 > 0,

you need to enter solve x ^ 2 + 3x-4<0 && 2x ^ 2 - x + 8> 0

Signs && in this case denotes a logical "AND".

5. Expansion of brackets + casting of similar ones in the expression.

Example... To expand the parentheses in the expression ( c + d) 2 (a-c) and bring similar ones, you need

enter expand (c + d) ^ 2 * (a-c).

6. Factoring the expression.

Example... To factor the expression x 2 + 3x- 4, you need to enter factor x ^ 2 + 3x - 4.

7. Calculation of the amount n the first members of the sequence (including arithmetic and geometric progressions).

Example... To calculate the sum of the first 20 terms of the sequence given by the formula a n = n 3 +n, you need to enter sum n ^ 3 + n, n = 1..20

If you need to calculate the sum of the first 10 members arithmetic progression with the first term a 1 = 3, difference d= 5, then you can, as an option, enter a1 = 3, d = 5, sum a1 + d (n-1), n ​​= 1..10

If you need to calculate the sum of the first 7 members geometric progression with the first term b 1 = 3, difference q= 5, then you can, as an option, enter b1 = 3, q ​​= 5, sum b1 * q ^ (n-1), n ​​= 1..7

8. Finding the derivative.

Example... To find the derivative of a function f(x) =x 2 + 3x- 4, you need to enter derivative x ^ 2 + 3x - 4

9. Finding the indefinite integral.

Example... To find the antiderivative of a function f(x) =x 2 + 3x- 4, you need to enter integrate x ^ 2 + 3x - 4

10. Calculation of a definite integral.

Example... To calculate the integral of the function f(x) =x 2 + 3x- 4 on the segment,

you need to enter integrate x ^ 2 + 3x - 4, x = 5..7

11. Calculation of limits.

Example... To make sure that

enter lim (x -> 0) (sin x) / x and see the answer. If you need to calculate some limit at x tending to infinity, one should introduce x -> inf.

12. Research function and plotting.

Example... To investigate the function x 3 — 3x 2 and plot it, just enter x ^ 3-3x ^ 2. You will get the roots (the points of intersection with the axis OH), derivative, graph, indefinite integral, extrema.

13. Finding the largest and smallest values ​​of a function on a segment.

Example... To find minimal function value x 3 — 3x 2 on the segment,

you need to enter minimize (x ^ 3-x ^ 2), (x, 0.5, 2)

To find the maximum function value x 3 — 3x 2 on the segment,

you need to enter maximize (x ^ 3-x ^ 2), (x, 0.5, 2)

A short list of WolframAlpha notation and operators for solving problems online

+	addition
—	subtraction
*	multiplication
/	division
^	exponentiation
solve	solution of equations, inequalities, systems of equations and inequalities
expand	opening brackets
factor	factorization
sum	calculating the sum of the members of a sequence
derivative	differentiation (derivative)
integrate	integral
lim	limit
inf	Infinity
plot	plot a function
log ( a, b)	logarithm to base a the numbers b
sin, cos, tg, ctg	sine, cosine, tangent, cotangent
sqrt	square root
pi	number "pi" (3.1415926535 ...)
e	number "e" (2.718281 ...)
i	Imaginary unit i
minimize, maximize	Finding extrema of a function (lows and highs)

Basic commands for Wolfram Alpha

1. Solving equations, building graphs

• Arithmetic signs plus, minus, multiply, divide +, -, *, / Examples: 3 * 2, x * y, (a + b) / c

• Exponentiation "x to the power of a" x ^ a. Examples x ^ a, x ** a, (a + b) ^ 2, (a + b) ** 2, (a + b) ^ (2x + 1)

• Brackets. Actions in brackets are taken first

• Functions sin (x), cos (x), tan (x) = sin (x) / cos (x), cotan (x) = cos (x) / sin (x), sec (x) = 1 / cos (x), cosec (x) = 1 / sin (x)

• Functions log (x), exp (x), sinh (x), cosh (x), tanh (x), cotanh (x)

• Square root of "x" sqrt (x) or x ^ (1/2)

• To evaluate an expression, you just need to enter it. For example, the root of 2 will look like sqrt (2) or 2 ^ (1/2).

2. To solve the equation, you just need to enter it

For example, x ** 2 + 2x + 1 = 0

3. To plot a graph, you need to use the plot command

For example, let's use Tungsten to draw the function 2 ^ (- x) cos (x). This is done with the plot command.
We will get the following great picture.

From this picture, you can already judge the zeros of the function (solutions to the equation), you can imagine how the function behaves, etc. Better to type in the format

To plot several graphs on one coordinate plane (for example, to visualize the solution of systems of equations), with the value of the variable x in the interval (A, B), you need to use the command

plot [(f1 [x], f2 (x)), (x, A, B)]

For example, the command plot [(2a + 3, a ^ 3-2a ^ 2), (a, -3, Pi] gives such a picture for the intersection of curves
y = 2 a +3
y = a ^ 3 - 2 a ^ 2
in the range from -3 to pi.

3. To solve the equation "left side (x) = 0", type the command "Solve equation = 0"

or, better, in the Solve format ["left side of the equation" == 0, x]

Here, the left side is what is in the equation on the left, and on the right is zero. Replace "x" with your own variable (y, z, etc.)

Example: Solve the equation ax + b = d. Stuffing Solve Getting

At the same time, we pressed the button "show steps".

To solve a system of equations, use the command Solve [(equation1, equation 2), (variable 1, variable 2)]

Example: solve the system of equations 3x + 4y = 0, x * x-y * y = 1 for x, y solve [(3 x + 4 y == 0, x ^ 2-y ^ 2 == 1), (x, y)]

To solve the equation in integers, use the "in integers" command. For example: a squared plus b squared equals 25 in whole numbers.

4. To collect factors from a binomial (polynomial) f, type factor [f]

5. To expand the product f into terms, use the expand [f] command

6. To simplify the expression f [x], type the command Simplify]

For example, to simplify "e to the power of prearithm x":

Simplify [exp [log [x]]]

gives the answer x:

Wolfram Mathematica Neural Networks 1.0

Wolfram Mathematica Link for Excel 3.1.1

Wolfram classification

trainingset = (1-> 1.3.2-> 2.4.3-> 6.4);

p = Predict

You can classify data.

You can not just predict an object, but you can say what a specific value will be equal to.

WolframScript

WolframScript can work with files without local kernels using the Wolfram Cloud. Start by creating a text file using the cloud engine.

Create a script file called FindPath.wls using the cloud core as an interpreter with the following content.

Interactive Manipulation

The single function Manipulate gives immediate access to a huge range of powerful interactive capabilities. For any expression with symbolic parameters, Manipulate automatically creates an interface for manipulating the parameters. Manipulate supports not only mouse and keyboard manipulation, but also gamepads and other devices.

Class 1 | Overview systemsWolfram MathematicaandWolfram cloud

Only children know what they are looking for. They give all their days to a rag doll, and it becomes very, very dear to them, and if it is taken away from them, the children cry ...

LearnPress is a WordPress

LearnPress is a WordPress complete solution for creating a Learning Management System (LMS). It can help you to create courses, lessons and quizzes.

#! / usr / local / bin / wolframscript -cloud -print -format PNG samples = ImportString [$ ScriptInputString, "JSON"]; order = Last]; tour = samples []; Show, Graphics]]

The script can be executed from command line using local text file as input.

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Bridge integrates WordPress with the Moodle LMS

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