 In this video, we'll talk about Ease's interface and we'll work through our first example problem, which will consist of a couple of simple equations. When you open Ease for the first time, you'll be presented with a big primary window and then a single secondary window. I'm going to refer to these as secondary windows. Seems like good consistent nomenclature. Unlike, say, Photoshop, your individual files do not appear as secondary windows. If you want to have multiple files open in Ease at the same time and you don't want them to interact with each other, they need to actually be entirely separate instances of Ease. These secondary windows are all belonging to this single file and all of your data input and output will come through these secondary windows. So you have different secondary windows for different purposes. The equations window is where you'll be entering your equations, which, oddly enough, you do a lot in the engineering equation solver software. But you can access the other windows by clicking on this Windows button up in the title bar. The equations window is here. If you close it at any point, you can access the window again by clicking on that button. The other one that you'll use a lot when you're first starting with Ease is the solutions window. So the solution window is where your solutions are presented. The other windows become more useful when you get into some of the more complex features of Ease. For example, the plot window is where you will plot data. The tables window is where you input and output tabular data. The report window is where you might format a report given the information that you calculated. The Windows button is just one of many buttons up here on the title bar, and most of them are pretty straightforward. The file button contains commands for opening and saving your files and libraries. That's where you would generate a report if you wanted to or if you wanted to print your solved solution or your report. The edit button contains copy and paste functions and, most importantly, the undo and redo options. The search button contains commands for finding and replacing. The options button is a little bit more complex. That's where you have commands to set your guest values and bounds for your variables. That's where you would select the unit system. That's where you get information in and out of the user-supplied library functions. You can set the program preferences, etc. The calculate button contains the commands to check, format, and solve your equation set. The commands are also there to check the unit consistency of your equations and update your guest values if you want. The tables button is where you would access tabular data. So there are two big tables that you might use in Ease. There are parametric tables and there are lookup tables. The parametric table is pretty similar to a spreadsheet. You can set your equations to calculate variables based on changing of some selected variables. So if you were working on a power cycle, for example, and you wanted to calculate a thermal efficiency for several different input temperatures, you would use a parametric table for that. So you would select the thermal efficiency as one of your outputs in the parametric table, and then you would select the ambient temperature as your input in the parametric table, and then you could have the parametric table actually run all of the equations and calculate a new thermal efficiency for each one of the values that you input in the parametric table. If you wanted to plot, say, how one variable affected other variables, so if you wanted to generate a plot of that thermal efficiency versus input temperature, you would do that by creating a parametric table and then generating a plot from the parametric table. The lookup table is useful for storing user-supplied data that you want to interpolate between. So if you were using a custom material and you had a lot of material properties and you wanted to generate information from those tables, you would enter that data as a lookup table. The Plots button provides commands to prepare a new plot of data from the tables, and you can also access some of the plots that you've already created. Most importantly, in my opinion here, there's also a property plot, which unlike a regular plot, can show your data relative to information about the property or information about the material. So if you wanted to plot thermodynamic state points relative to saturation lines, you would do that within a property plot here. The Windows button we've already talked about, that's how you access the different sub or secondary windows, whatever I decided to call that. The Plots button contains a lot of actually extremely useful information. You can access the help index, which is very, very useful. If at any point you're trying to figure out how to do something in ease and you can't find one of my videos to explain it to you, you might search for it in the help index. So for example, if you were trying to remember how to solve a differential equation, you could open up the help index and then just type in differential equation. Now ease has a nice explanation of how to go about doing that and what the different variables mean in the different functions. Help index is very useful. There are also commands here to open up YouTube tutorials that the manufacturer of the software created and posted on YouTube. You can also get to their website directly from a button here. If you've purchased the Mastering Ease book, you can access your book directly from this interface, etc. The Examples button is also extremely useful, especially when you're first starting out, because this contains just a whole bunch of example problems for different situations. Each one of these buttons will actually open up another window where you can select an example problem. So if you were trying to figure out how to run differential equations, if you click on differential equations, you open up a window with all of these example problems. Each one of these is a full-fledged ease problem. So if you clicked on it, it would open up that window. So the example problems are also very useful. Let's get back to our blank file. Also note that sometimes the options available in these drop-down menus can change based on which version of the software you're running. So if you're following along with one of my videos and you don't see a button that I clicked on, it's probably because you're running a different version of ease. Again, I'm running the academic professional version. So back to the equations window. You type in equations in the equations window just like you would in a text editor. For example, if I was trying to solve two equations with two unknowns, let's say the first equation was x squared plus y is equal to 16, and x minus y was 7, let's say. I type those in like this. Then when I want to solve the equations, I click on the solve button. So you can access the solve button by going up to calculate and then solve. A lot of these functions within these drop-down menus are also presented in the toolbar up here, but you always have more options available to you by going up to the actual drop-down menu. So from the toolbar, we could select the solve button or the check equations button or the min-max functions here, but if we actually went up to calculate, we have those options plus a lot more. So when you're learning how to use ease, I think it's better to get used to these drop-down menus, and then you can think of the toolbar up here as shortcuts rather than your options, if that makes any sort of sense. But anyway, we have our two equations, two unknowns. The best procedure here would be to click on this check mark first. The check mark will check your equations and it will tell you if you have any typos, etc. before it commits to actually solving the program. Again, when ease solves, which I can do by clicking on the solve button, it actually guesses values for the unknown variables and then it proceeds to guess and check until it decides that what it guessed was the correct answer. And the way that it decides whether or not its answer is correct is based on residuals, which is the difference between the different guess values. So once it gets to a point where it's not changing its guess values very much, a threshold that you can control, then that is how it decides that that answer is correct. So that can take a long time if you're running a lot of equations on a slower machine. But here I have two equations with two unknowns and that took 0.0 seconds. So the answer to my two equations problem was that x is equal to 4.322 and y is equal to negative 2.678. You'll notice that I typed in x squared by typing x and then a carat and then the number 2. The carat represents the exponent operator in ease and it's just one of many operators or many formatting rules that ease has for entering equations. So I'm going to dump a whole bunch of formatting rules on you right now, at least the ones that I'm familiar with, so prepare yourself. First up, upper and lower case letters are not distinguished. Ease will optionally change the case of all variables to match the manner in which they first appear. So for example, if you were running a problem and you had both volume and specific volume or say volume and velocity, you might be tempted to type those in with a capital V and a lower case V. So you could say my volume is 10 cubic meters and my velocity is 3 meters per second. If you type them in like this, ease thinks that those are the same variable. It does not distinguish between lower case and capital letters. If I were to try to solve this right now, ease would throw up an error. That error would be because I overdefined V. I told that V was 10 and I also told that V was 3. I'd have to come up with a way to distinguish the variable names from each other. But variable names don't have to just be a single letter. They can actually be up to 30 letters. So I could type in the word volume and have that be my variable for volume or I could type in the word velocity for my velocity variable. Two, blank lines and spaces are ignored by ease. So you'll notice that I typed in my two equations with this blank line between them. That was just a way that I kept my two equations separate. It's kind of a personal organization thing. The blank line is ignored, so I could have as many blank lines as I want and ease would see this as exactly the same as earlier. It still sees it as two equations. I could also use spaces to keep my equations organized. I could say increase the indent here if I wanted to. I personally use that for hierarchical equations. For example, if I had the same equations for different state points, I might say state one and then have my equations for state one and then I might have state two and then have equations for state two like this. I think that it's an easy way to keep things organized. And speaking of keeping things organized, you can use comments and ease. And comments work the exact same way as they do in any programming language. And in ease, they are denoted by either quotation marks or curly brackets. And comments are ignored by ease. They are intended to present information to humans. So I could put a comment in above my first equation and say, this is the first equation. And I could put in a comment above my second equation that says, this is the second equation. And ease will ignore those two lines because they are in quotation marks. So if I were to run this now, you'll notice that ease changes the color of those two lines. It color codes information in your equations window. If at any point you want to trigger the color coding, you can actually do that by just checking the equations. You don't actually have to click the solve button. But if you wanted your comment to span multiple lines, you just place the start and end comment operators, denoters. You place the symbols on separate lines. So in this case, this is the second equation comment actually spans these five lines. So that can be useful for entering just a whole bunch of information, like say a problem statement. But it's also useful for adding in extra information to your comments. For example, I use equations, excuse me, equation marks like this, equation signs as a means of keeping my file organized. So if I wanted to clearly partition off sections of my equations window, if I wrap them with equation symbols like this, that's an easy way to do that. It just sort of stands out. And again, because they're within quotation marks, ease ignores them. I personally will be using the curly brackets in my examples a lot more than I will the quotation marks. And my logic on that is a little odd. I think it probably only makes sense in my brain. But the quotation marks are the same symbol. The same symbol opens and closes the comment. So think of a situation where I had a lot of comments. So I had these two comments and then maybe a third comment at the end that said, this is the end of the equations. So this is the end of the equations. Well, let's say that I had forgotten this quotation mark. Now ease still sees this as three comments, but it starts the comment with the first quotation mark it sees, and then it ends the comment with the next quotation mark it sees. So if I had forgotten this quotation mark, ease now sees this as the first comment and this as the second comment. That can be a little bit difficult to debug because now ease sees this as a second equation and it thinks there's a variable this and a variable is and a variable the and a variable second and it doesn't see any operators between them, so it doesn't know what to do. If I were to hit solve now, it would probably panic. Yes. Then it sees this last quotation mark as starting a third comment, which is never closed. So by using curly brackets instead of quotation marks, you have a different symbol to start the comment and a different symbol to end the comment. So in the event that you forget one of your symbols, it's a really convenient way of keeping track of them, at least in my opinion. Another shortcut for using comments is if you highlight whatever region you want to declare a comment or to uncomment, you can right click and activate or deactivate the comment symbols here. That's a very convenient way of temporarily disabling an equation when you're working through a file or if you want to switch back and forth between two equations. So let's go back to quotation marks and remove this line. Then we'll proceed on to number four. Variable names must start with a letter and can consist of any keyboard characters except for those symbols which have some other meaning within ease. So that shortlist is these characters. You cannot use any of those characters in your variable name because that goes back to how ease ignores spaces. For example, I could have typed in my second equation by typing in x minus y equals seven with no spaces. So you might think of this as a variable if you were trying to use the minus and equal signs in part of your variable name, but ease would parse that out as an equation. So you can't use any symbols that have some other meaning to ease. Number five, equations can be as long as you want. If you want the equation to actually span multiple lines, you would separate the lines with a semicolon. Number six, the caret symbol is how you denote an exponent. So like I said, caret two here, ease will treat that as x squared. If I typed e to the fifth, that would be, or x to the fifth, that would be parsed out as x raised to the fifth power. If I were to put parentheses here, I can group other operations within that exponent so I could say, for example, five plus y. And now that'll be parsed as x raised to the five plus y power. If I wanted to have say, x to the k minus one over k, I would have to use multiple parentheses to do that. If you want, you can actually use two asterisks, x to y, asterisks. You can use two asterisks instead of the caret symbol if you prefer. Ease will still use that as an exponent operator. Number seven, the underscore symbol is used to indicate a subscript. So if I were to type, say, m underscore one is equal to five. Ease will parse that as m with a subscript one. You can make that be multiple symbols if you want. Say, m the first. And if you wanted to have a common, or rather a comma up here in your subscript, you would use another underscore for that. So I could say the specific net work out like this. Ease would see that as a w with a subscript and that subscript is net comma out. The underscore is also used to modify variables. There are special variable modifications that are listed in their entirety in the ease manual. I use dot and bar a lot. So x underscore dot will appear as an x with a dot above it. X underscore bar will appear as x with a horizontal line above it. Like this. So if I wanted to write the net power output, I could do that by saying capital W dot net out. So it sees w underscore dot and it'll use a w with a dot above it for that. And the next underscore triggers the subscript and then the third underscore is a comma within the subscript. Like this. So net power output. You can also include other symbols within the subscript if you like. So if you wanted to have a variable for the heat transfer in occurring between two and three, you could type that like that. So it would appear as q in comma to arrow three. Next up, Greek letters. Greek letters are denoted in ease by actually typing the name of the Greek letter. The downside here is you need to know how to spell your Greek letters or rather spell the word that we use to represent the Greek letter. So for example, if you were working through a problem and you had a density appear, you would probably denote that with a Greek letter row. So you would make that appear in ease by actually typing the word row. So if I typed row equals five, that would appear as the Greek letter row. And ease differentiates lowercase Greek letters and capital Greek letters with lowercase and uppercase words. So if I typed a lowercase rho, that would appear as the lowercase Greek letter row. If I typed capital rho, ease would see that as the uppercase Greek letter, which apparently looks very similar. Okay, that's boring. Let's go with a fancier one. Delta. Let's say delta. A lowercase delta will appear as that thing that looks kind of like a two. Yeah, that looks kind of like a two, right guys? And if I were to type the word delta in uppercase, that would appear as a triangle. If you want to have more than one symbol, rather a Greek letter and then some other symbols appear in your variable name, you don't put spaces between them because that would separate the variables. You just continue the name of the variable. So for example, let's say that I had m underscore one is equal to two and m underscore two is equal to five. And I wanted to show the difference in my mass. I would type delta and then m immediately after it. And I could denote that as m two minus m one. So ease will show delta and then an m immediately after it. And again, because that delta is written in uppercase letters, ease will use the uppercase delta for that symbol. But just like with the other characters, if I were to type delta equals five and uppercase delta equals two, ease will see this as over defining the same variable because the lowercase and uppercase variable are not distinguished from one another. I could combine these formatting rules in my equations if I wanted to. For example, if I were to type eta underscore th, that would appear as the eta symbol with a subscript th. Or if I wanted to have say eta underscore alpha, that would appear as the Greek letter eta with a subscript of the Greek letter alpha. The last thing I want to talk about in the formatting rules is that the order of the equations and the order of the variables does not matter to ease. So I could put this equation first and this equation second if I wanted to. It makes no difference to ease. It solves them all simultaneously. Also the order of the variables does not matter. So I could write ease minus y, or ease minus y. X minus y is equal to seven. I could just as well write x equals seven plus y. And that will end up being the exact same thing to ease. The one exception to that is when you're typing equations, if you had something appear maybe like this. Let's say I could write this equation as being x is equal to seven over y, or x times y is equal to seven. Well, remember that the way ease solves for variables is to guess values and then guess and check until it decides that what it guessed was correct. Here, if I happen to begin a situation where ease guessed a value of zero for y, it would quit and have an error here. So when you have variables appear in a denominator, that can sometimes be dangerous, or other situations where you run into a mathematical uncertainty or impossibility. So if I had x times y, that is the same way of writing the equation, but this is a little safer, because if ease guessed a value of zero for y, then it would be able to continue its operation. That's not something you probably need to worry about often, but that'll show up when you least expect it. The best practice is to type denominators as a numerator on the other side of the equation, if that makes any sort of sense whatsoever. Another tool that's very useful when you're learning the formatting rules is the formatted equations window. So if I had gone back to my example of x squared plus y's, no, this would be x minus y. So if I had x minus y is equal to seven, if I open up the formatted equations window, that will show the equations with the formatting rules applied, like this. So it shows x to asterisks is two x with a superscript of two. That's a very convenient way to get, I guess, a better view of your equations. It makes it easier to see your relationships between your equations. When you're running a program that has a lot of equations in it, it can just end up turning into a giant wall of text. So the formatted equations window is presented in a more aesthetically pleasing way that's also more useful. So let me give it something complicated here. Say I had a third equation that was z is equal to the x minus one over y minus one. Then the formatted equations window will show that as separate lines. So I could also wrap these in more parentheses and say raise to the k minus one over k. Now you see how these symbols start to blur together. If I go up to formatted equations, it's shown in a slightly more readable way. So that concludes this video. Next time on Ease Tutorials, we'll talk about a more complex example problem. We'll get into an actual realistic problem, say something involving the ideal gas law, and we will incorporate units into our equations. Stay tuned.