Specific Kinds Of Variables
It is common for variables to play different roles in the same mathematical formula, and names or qualifiers have been introduced to distinguish them. For example, the general cubic equation
- a , +bx^+cx+d=0,}
is interpreted as having five variables: four, a, b, c, d, which are taken to be given numbers and the fifth variable, x, is understood to be an unknown number. To distinguish them, the variable x is called an unknown, and the other variables are called parameters or coefficients, or sometimes constants, although this last terminology is incorrect for an equation, and should be reserved for the function defined by the left-hand side of this equation.
In the context of functions, the term variable refers commonly to the arguments of the functions. This is typically the case in sentences like “function of a real variable“, “x is the variable of the function f: x f“, “f is a function of the variable x” .
In the same context, variables that are independent of x define constant functions and are therefore called constant. For example, a constant of integration is an arbitrary constant function that is added to a particular antiderivative to obtain the other antiderivatives. Because the strong relationship between polynomials and polynomial function, the term “constant” is often used to denote the coefficients of a polynomial, which are constant functions of the indeterminates.
Other specific names for variables are:
Best Way To Write An Equation With Subscripts And Superscripts
This post is not about a specific Mathematica problem but about to develop the best way to enter mathematical equations with subscripts and superscripts. I have a model of a large number of equations in which variables have subscripts, superscripts, and an index to create a set of equations using Table.
I wonder if anybody can suggest me the best way to enter model equations such as those in dynamic stochastic equilibrium models. Equations have all kinds of subscripts and superscripts, and I like to know the best way of writing such equations in Mathematica.
EDIT 1Here is an example of a model I aim to solve. Using the suggested subscript and superscript notation to write a Mathematica code will be very complicated and there must be another way to code this model because Mathematica is supposed to be powerful solve much more complicated and larger system of non-linear equations.
As can be easily seen from this example model, I could log-linearize the model and redefine the variables and solve the system. My question is not about solving this model but entering the model equations in an efficient format using Mathematica. It is obvious to me that using long-subscript and superscripted variables is not the way forward. I am interested in a robust and stable coding of model of this kind.
I hope my question is clear.
Reserved Characters And Keywords
Most characters and numbers on the keyboard can be used at their default value. As with any computing language, though, there are a set of reserved characters and keywords that are used by the program for its own purposes. TeX Notation is no different, but it does have a very small set of Reserved Characters. This will not be a complete list of reserved characters, but some of these are:
To use these characters in an equation just place the \ in front of them \$ or \%. If you want to use the backslash, just use \backslash. The only exception here seems to be the & , ampersand. See the characters listed in Using TeX Notation 2 for more details.
The Keywords, they are different. There is only one that is of concern here and that it the word “line”. If the \line control sequence, or command, is not properly implemented, then the consequences can be indeterminate. Controlling lines is an adventure of its own, so getting it right when written is important, you can always reposition the line, but you might get it really wrong if you do not use it with some caution.
To use the \line control sequence, go to your text editor, open the filter\lib.php file. In this file look for the array $tex_blacklist = array(, and in the list of words that follow, you will see the word “\line”. Delete the word, with its enclosing single quote marks and trailing comma, from the list.
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Using Tex Notation With The Moodle Tex Filter
For the most part, the TeX Notation has been built using a sub-set of characters from the TeX “default” character set. The trouble is there does not seem to be a “default” character set for TeX. This is one of the most confusing aspects of using TeX Notation in Moodle. When we realise that the documentation we are using is related to the creation of printed documents, and we want to use TeX on line, in Moodle, then further problems occur. There are no environment statements to be made. There are few \begins and \ends. If you go to Administration > Modules > Filters > Filter Manager you will see what filters have been enabled. If you then go to the TeX Notation page, the default preamble is editable via the text box. Using this tool you can add in or subtract font packages and other packages, change the default font package, etc.
Genesis And Evolution Of The Concept
At the end of the 16th century, François Viète introduced the idea of representing known and unknown numbers by letters, nowadays called variables, and the idea of computing with them as if they were numbersin order to obtain the result by a simple replacement. Viète’s convention was to use consonants for known values, and vowels for unknowns.
In 1637, René Descartes “invented the convention of representing unknowns in equations by x, y, and z, and knowns by a, b, and c“. Contrarily to Viète’s convention, Descartes’ is still commonly in use. The history of the letter x in math was discussed in a 1887 Scientific American article.
Starting in the 1660s, Isaac Newton and Gottfried Wilhelm Leibniz independently developed the infinitesimal calculus, which essentially consists of studying how an infinitesimal variation of a variable quantity induces a corresponding variation of another quantity which is a function of the first variable. Almost a century later, Leonhard Euler fixed the terminology of infinitesimal calculus, and introduced the notation y = f for a function f, its variablex and its value y. Until the end of the 19th century, the word variable referred almost exclusively to the arguments and the values of functions.
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Sums Products Limits And Logarithms
Use the commands \sum, \prod, \lim, and \log respectively. To denote lower and upper bounds, or the base of the logarithm, use _ and ^ in the same way they are used for subscripts and superscripts.
Some of these are prettier in display mode:
Note that we can use sums, products, and logarithms without _ or ^ modifiers.
|9\equiv 3 \bmod|
|9\equiv 3 \pmod|
|9\equiv 3 \mod|
|9\equiv 3 \pod|
Subscripts That Are Aligned With The Baseline
The only common use of these subscripts is for the denominators of diagonal fractions, like Â½ or the signs for percent %, permille â°, and basis point â±. Certain standard abbreviations are also composed as diagonal fractions, such as â
These superscripts typically share a baseline with numerator digits, the top of which are aligned with the top of the full-height numerals of the base font lowercase ascenders may extend above.
Ordinal indicators are sometimes written as superscripts , although many English-language style guides recommend against this use. Other languages use a similar convention, such as 1er or 2e in French, or 4Âª and 4Âº in Portuguese, Galician and Italian, or 4.Âª and 4.Âº in Spanish.
In medieval manuscripts, many superscript as well as subscript signs were used to abbreviate text. From these developed modern diacritical marks . Also, in early Middle High German, umlauts and other modifications to pronunciation would be indicated by superscript letters placed directly above the letter they modified. Thus the modern umlaut Ã¼ was written as uÍ¤. Both vowels and consonants were used in this way, as in Å¿heÍ¨zze and boÍ®sen. In modern typefaces, these letters are usually smaller than other superscripts, and their baseline is slightly above the base font’s midline, making them extend no higher than a typical ordinal indicator.
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Highlighting Subscripts/superscripts In Math Mode
This is an extension of Highlight terms in equation mode,
The problem is, with
In, $x^}$, \alpha is enlarged abnormally, unlike a proper superscript.
Is there a way to highlight specific variables within math-mode whilst maintaining subscripts and superscripts?
- Does \scriptsize\alphawork for you? user193767May 8 ’20 at 12:06
- $a^} does not workMay 8 ’20 at 12:11
- 1$a^}$, maybe? It works here. user193767May 8 ’20 at 12:12
- Yes it works! Thank you very much.May 8 ’20 at 12:14
- No problem! Stay safe
Your \highlight command doesn’t work in superscripts because the equation in the \colorbox doesn’t know it’s supposed to be typeset in \scriptstyle and because of the \displaystyle in its definition explicitly telling TeX to typeset #1 in display style .
This is pretty much exactly what the \mathpalette command is designed to solve.A detailed description of how \mathpalette works can be found here.
Here is a simple re-implementation that uses `\mathpalette.
What \highlight now does is expand to \highlightwithstyle, where < current math style> is either \displaystyle, \textstyle, \scriptstyle or \scriptscriptstyle . This in turn turns into
when used in a super-/subscript, and into
when used in the main display equation etc.
Dependent And Independent Variables
In calculus and its application to physics and other sciences, it is rather common to consider a variable, say y, whose possible values depend on the value of another variable, say x. In mathematical terms, the dependent variable y represents the value of a function of x. To simplify formulas, it is often useful to use the same symbol for the dependent variable y and the function mapping x onto y. For example, the state of a physical system depends on measurable quantities such as the pressure, the temperature, the spatial position, …, and all these quantities vary when the system evolves, that is, they are function of the time. In the formulas describing the system, these quantities are represented by variables which are dependent on the time, and thus considered implicitly as functions of the time.
Therefore, in a formula, a dependent variable is a variable that is implicitly a function of another variables. An independent variable is a variable that is not dependent.
The property of a variable to be dependent or independent depends often of the point of view and is not intrinsic. For example, in the notation f, the three variables may be all independent and the notation represents a function of three variables. On the other hand, if y and z depend on x then the notation represents a function of the single independent variablex.
If one defines a function f from the real numbers to the real numbers by
- 2 ^i=+n}}}
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What Does It Mean When A Letter Has Both Superscript And Subscript
I have a formula for Bond Valuation of a Level Coupon Bond, but I don’t understand the notation. It looks like:
It’s the bottom formula in the image below, starting with PV =
What does it mean when the A has both T and R next to it?
- $\begingroup$The T means $A_R$ to the T-th power. The R is an index. It means that somehow the value of $A_R$ was determined or related in some way to R. $A_R$ is just a variable. $A_R^T$ is just a variable raised to the T-th power.$\endgroup$ fleabloodJan 20 ’16 at 18:34
- $\begingroup$Okay. So you calculate it based on A? Like if A is, 5, and T is 2, it’s just 25? Sorry for my inexpertise, I don’t study finance.$\endgroup$ LouJan 20 ’16 at 18:36
- $\begingroup$Just based on what’s being computed here, I’d have said $A_R^T$ was the present value of a stream of $T$ periodic payments of $1$ euro discounted at $R$.$\endgroup$ luluJan 20 ’16 at 18:46
- $\begingroup$I’ve changed my mind. I think that it’s a way of notating that the value A is determined by R and T so depending on what R is and what T is you have a value $A_$ and $A_R^T$ is another way of writing that. $A_R^T = 1/ + 1/^2 + ….. + 1/^T$. You can think of this in two equivalent ways: A is a function of R and T: or there is a 2-dim grid of values and $A_R^T$ is the entry in the Rth column and the Tth row. Or I could still be wrong.$\endgroup$Jan 20 ’16 at 18:54
- $\begingroup$Could you zoom out so we can see the whole equation above it?$\endgroup$
Studying Algebra Is Stupid
Have you ever asked yourself why do people always complain about math and science? Is it because they require a lot of discipline and dedication? Or because theyre difficult to understand?
Have you ever noticed that no one asks why you have to take physical education or English literature classes, even though math, physics, and science are much more critical to the founding of the modern society than Shakespeare or the techniques of shooting a three-pointer?
Education has to be fun, easy, and entertaining in order for it to be acceptable, or so says the modern American educationist philosophy.
Todays students believe that if a subject requires some effort, they shouldnt have to take it. Little do they know that the most beneficial things in life demand making some effort.
If you want an excellent job, an alluring career, a limitless future, youll most definitely be in need of some mathematical skills, and when you say math, you say algebra.
Have you ever thought about why do you hit the gym regularly? Is it because lifting weights is effortless? Or because you want to get better, challenge yourself, build your strength, and prepare your body for whatever you might encounter in life?
Why do people cycle or jog? Is it because its fun to sweat bullets and get knee soreness? If I were to guess I would say that they do it because they want to be healthy and strong in order to resist diseases and be ready for whatever health obstacle life may throw their way.
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How To Set Subscript And Superscript Text In String
I’m working on an Android app, and I need to be able to include the exponents/powers into a string . I’ve done some searching and it seems that my scenario is making it difficult. I’ve looked into options such as ALT+ codes and Unicode. I’m not entirely sure if either of those, or any other options, are actually possible .
So, what’s my best option, if any?
I’d like to keep it as simple as possible. I have a lot of strings to write and the need to subscript/superscript numbers is random. Can this be done easily?
EDIT: I suppose I was vague. My app is for studying. And the questions/answers are put into arrays and randomized each time. I’d like to be able to set the strings in the Java file as they are now
question.text = "solve x^2 if x=5"
But instead of the user seeing “^2”, I’d like to use the actual superscripts.
question.question = "Question Text. I would like to add a superscript or two here, as if it were a math problem" question.answer. = "Answer 1. Add a subscript here" question.answer. = "Answer 2. Add another superscript here." question.answer. = "Answer 3. Etc." question.answer. = "Answer 4. Etc."
//SET QUESTION STRING TO TEXTVIEW textQuestion.setText) //SET ANSWER STRINGS TO BUTTONS' TEXT buttonOne.setText) buttonTwo.setText) buttonThree.setText) buttonFour.setText)
Will I Really Need Algebra In Real Life
Sadly, we cannot answer that question for you. Its not a simple yes-or-no situation.
Think of the rate of non-traditional students retaking math classes, and all the old people returning to uni after years of dropping out, even though they dont need algebra for their jobs.
The very fact that they are studying algebra all these years after high school highly indicates that they havent used algebra a lot since the time they finished their studies. They made it this far without needing algebra, but here they are returning back to the very college seats they abandoned years ago because they felt the necessity of such a subject.
Take into consideration that you didnt learn the alphabet back in kindergarten because you knew youd be studying Shakespeares plays this year. The same goes for algebra you dont study it because you know that youll be interpreting graphs and working with quadratics in a few years, you study it to build the cornerstone for bigger things to come, and to help create better opportunities for yourself in the future.
Algebra is the key to various domains no matter how big or small they are.
For instance, lets assume that your job requires working with spreadsheets filled with formulas. For that, you need a basic understanding and enough knowledge of variables and equations.
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