#### Calculator Guide by Talen Phillips

Version 1: 19AUG2015

#### NULLA. Intro

This guide is meant primarily for students, but can certainly be used by practicing engineers, plenty of whom seem to use scientific and graphing calculators alongside software packages like

MathCAD,

Mathematica,

Maple, etc. It is not intended to be a full review of any of these calculators (many of which I have limited experience with).

The reason I'm writing this guide is because I find that being very familiar with my tools helps me spend a little less time doing tedious calculations and more of my time actually focusing on understanding material. I highly recommend other students pay a little more attention to their calculators so they can make the most of them.

I've tried to remove my personal biases, however some calculators are actually better than others. This doesn't mean the others aren't capable of getting you through your degree. In fact, ANY of these calculators will do the job. Hell, even a slide-rule could work. However, being able to compute directly with complex numbers, evaluate definite integrals and derivatives, work with matrices, find the roots of polynomials, and solve systems of equations is a HUGE advantage in certain classes.

Generally speaking, all you really need is one of the calculators from section 3. Graphing and

CAS aren't required. YMMV

#### I. Terminology

There are three main styles of input that we'll discuss here. Others exist, but since they aren't used by these calculators, they've been omitted.

**Algebraic** is what most people are familiar with. It is also known as

“infix notation”. The operators go between the numbers just as you would write it, and the calculator uses parentheses to resolve any issues with the order of operations. The only downside is that the entire equation is on one line, without the ability to show numerators and denominators or full integrands as you would write them. For example, if you want to enter a fraction which has a sum in the numerator and a difference in the denominator, you enter: (a + b)/(c - d). This is less than ideal. In fact, it's the worst input method I'll discuss. It requires more keystrokes, more forethought, and often can't be displayed appropriately on the calculator.

**Textbook-style** input is exactly what it sounds like. All functions are displayed on your calculator exactly as they would appear in a textbook, or how you would write them on a page. If you want the expression above, on most calculators of this style you would type [fraction button], a, +, b, [down arrow], c, -, d. The fraction would then be displayed without parentheses just as you would write it. Having the expression displayed clearly like this aids in thinking and allows easy editing even after the fact (typically you can use the arrow to select and edit expressions you've already evaluated).

Textbook-style input is also known as “Mathprint” on TI calculators, “Natural-V.P.A.M.” or “Natural Display” on Casio calculators, and “Writeview” on Sharp Calculators.

**RPN** (also known as

postfix notation) is the black sheep of the family (though many older engineers swear by it), and is only used by one of the major calculator manufacturers (HP). It is ostensibly the fastest method of input, but you really have to be fluent in RPN to take advantage of the extra speed. I'm not sure I'll be able to give a comprehensive explanation here, so I won't try. The short version is that it works very much like a computer's stack. You push numbers into the stack with an enter key, and when you hit an operation that works with N numbers (typically 1 or 2), the first N numbers are popped out of the stack, the operation is performed, and the result is pushed back into the stack. Note that HP's metaphorical stack pointer points to the bottom, and elements are pushed UP into the stack.

The input sequence for our fraction would go: a, [enter], b, +, c, [enter], d, -, /.

**Opinion:** Unless you feel particularly adventurous, hipster, or you think in terms of stack elements, it's probably best to stick with Textbook-style input. It has the strong advantage of allowing you to see previously used expressions and edit them.

#### II. Basic Scientific Calculators

Examples:

TI-30 series,

Casio fx-300,

Sharp EL-W531X The calculators in this category have decent functionality for the most part. They all cover trigonometric functions, logarithms, exponents, and most can do some fairly advanced statistics and even have a few probability functions. However, they're missing some key features that the advanced scientific calculators have.

I generally advise other engineering students to

**avoid these calculators**. It's only a few dollars difference to get a much, MUCH more powerful model. If you must get one, try to get something like the

TI-30XS MultiView, Sharp Writeview (denoted with a W in the model number), or the Casio fx-300, all of which have textbook-style input.

#### III. Advanced Scientific Calculators

Examples:

TI-36 series,

Casio fx-115 (known as the fx-991 in the EU), HP

33s/

35s,

Sharp EL-W516X or

EL-W506X These calculators have all of the functions of the basic scientific calculators, but also handle

**numeric integration and differentiation, matrices, and complex numbers**. Note that not all functions will work in the complex domain. All of the calculators I listed except the Sharp are allowed on the Fundamentals of Engineering exam in North America. I haven't used the Sharp, but I own the HP, TI, and Casio. All of these calculators except the HP cost between $10 and $20 in the US. The HP costs $50.

The

**TI-36 and the fx-115** are roughly equivalent in terms of functionality. It's hard to find something that one can do but not the other. Both of them are about as capable as a TI-84, except without graphing, programmability, and limited matrix size. There are three main differences that lead me to recommend the TI over the Casio.

- The Casio has different modes for different kinds of calculations. For example, complex numbers require complex mode, which doesn't allow integrals. The TI has one workspace for most of its calculations.
- The TI has a fantastic layout. Maybe I'm just used to TI calculators or maybe it's the "cycle keys" (push once for pi, again for e, and again for i), but I like working with the TI much better.
- The TI is about 3x faster than the Casio. This won't matter for typical calculations, but if you ever have to evaluate a complicated integral like the gamma function, you'll be happy to have the TI.

**The HP 35s** is another beast ENTIRELY. It uses RPN as mentioned earlier. There is an algebraic mode, but I really recommend against using algebraic mode on an HP calculator. It handles complex numbers much better than the TI or Casio calculators (they can be used in exponential and trigonometric functions). The integration interface is a little clunky, but it works. It's keystroke programmable (very, VERY easy to learn), so you can often set up a small program in just a few seconds to take care of some tedious task.

The programming aspect makes the HP calculators a step up from the others on this list. There are already programs to do many things that the other calculators can't do (such as solving systems of complex-valued linear equations), and there's PLENTY of room for more programs. I'm told that the memory doesn't get reset by the test center, but I can't confirm that.

**The Sharps** I've seen in the past looked like knock-offs of Casio calculators, but the current models look different (and pretty!). I have no idea what they're like, so I won't say more. (if anyone else discusses them, I'll edit it in)

There are others that have been left out such as the programmable Casio models, but they're not allowed on the FE or PE, and this (to me) is the point of using a non-graphing calculator.

#### IV. Non-CAS Graphing Calculators

Examples:

TI-84 (in all of it's incarnations),

TI-83,

Casio 9860GII,

Casio PRIZM fx-CG10/fx-CG20

This category is for your oldschool, run-of-the-mill, graphing calculators. These are for when computer algebra systems (CAS) aren't allowed by your professor... but graphing calculators somehow are. I want to start off by saying that

**YOU DO NOT NEED A GRAPHING CALCULATOR FOR ENGINEERING!** If you ARE going to get a graphing calculator, I strongly recommend you go all in with an advanced CAS model.

With that aside, I can point out the benefits of having such a beast.

- First of all, I have yet to see a graphing calculator that wasn't programmable (although I'm sure they exist). Creating your own programs is extremely nice for learning concepts inside and out, and for saving yourself a couple of minutes on a test if you're really prepared for it.
- They typically come with software for all kinds of things. Yes you can play games on them, but you can also use that financial app when you're taking econ.
- Where Advanced Scientific calculators will support up to 3x3 matrices, most of these will support MUCH larger matrices (though still not complex matrices).
- These calculators aren't solar powered. They have lots more juice to run through their processors, and can therefore do computations much faster.

Obviously the

**TI-84** dominates this category. In fact, that's the one I recommend you get if you must get something from this category. There are a bunch of iterations, but they all have almost exactly the same functionality. The latest edition is the TI-84 Plus CE, and it has a fancy, high-res, backlit, color screen and a rechargeable battery. If you're not getting a used TI-84, get the CE.

If your school supports Casio, feel free to pick up the

**PRIZM**. I have no experience with it, but the display looks really nice.

I haven't used the

**non-CAS nSpire** models, but I can't really see a good reason to use them, since the TI-84 CE will be more test compliant, and probably faster.

#### V. CAS Graphing Calculators

Examples:

TI-89,

HP 50g series,

TI nSpire CX CAS,

HP Prime Here we enter into the wonderful world of Computer Algebra Systems.

**Disclaimer: I am not responsible for your laziness. Having a fancy CAS calculator isn't an excuse to not learn how to do partial fractions or laplace transforms.** You should know how to do symbolic stuff like that efficiently by hand. If you do, then these calculators are a GREAT way of checking answers and exploring problems. They're all programmable, they all come with awesome software, and they all have powerful graphing abilities. (they also handle complex matrices, which is extremely useful)

I considered splitting this category into basic and advanced, but the newer calculators don't do THAT much more than the older CAS models, so it all goes into one category.

The

**TI-89, and HP 50g** are the oldest of this bunch in terms of technology, but they were made specifically for engineering students and practising engineers. The TI is certainly more user friendly (IMO), but the HP models tend to have a bit more functionality (though you can get software for both). None of these have whizbang color screens or touchpad/touchscreen interfaces. They're just monochrome displays. They both run on AAA batteries, and have a long battery life.

*Interface*: The main difference between the TI-89 and HP 50g is the input style. The TI-89 has an algebraic input. The HP is firmly based on RPN, though it supports algebraic and has a decent equation writer that can serve as a clunky textbook-style input. RPN is by far the preferred input method for the HP. *Programming*: The TI-89 can be programmed with a TI version of BASIC, or with assembly, though there are resources that allow for C programming (kind of). Meanwhile the HP 50g can be programmed in RPL or assembly, and there are resources that allow for C programming (again, kind of). *Connectivity*: The HP 50g actually has much more connectivity with the outside world. It has a USB port, an SD Card slot, a serial port, an irDA port, and even a buzzer (IDK just go with it). The TI-89 has a USB port and a port for connecting to other TI calculators. *Price*: The TI-89 Titanium usually costs ~$140, meanwhile the HP 50g can be had for ~$75.

Either of these machines will do whatever you need. Both are solid choices.

The

**TI nSpire CX CAS** is TI's latest offering. It's fast, has a fancy screen with a touchpad controlled mouse, and runs on a rechargeable battery. Like the TI-89, it gets plenty of support from TI and the community. There are plenty of apps to do whatever you need. It supports textbook-style and algebraic input styles, and is fairly user friendly (lots of drop-down menus). If you're looking for a CAS calculator, this is a solid choice. Be aware that some teachers will disallow the nSpire, even though they allow the TI-89.

The

**HP Prime** is (to my knowledge) the most recent calculator technology. It was released in 2013 (vs 2011 for the nSpire). It sports a high-res

*multi-touch*, backlit, color display and a rechargeable battery. The calculator runs on a MUCH faster processor (ARM 9) than anything else here. It's

*at least* an order of magnitude faster than the nSpire (which is already the second fastest calculator here). It supports all three input styles, but seems focused on textbook-style input (RPN isn't available in the CAS screen). It's a little less intuitive at times (though the contextual help button is VERY nice), but seems to have more functionality than the nSpire.

I just want to note that the touchscreen initially seemed like a gimmick, but turned out to be extremely handy. If you want to select a previous result, you just touch it twice, and it will appear in the command line where your cursor was. Is that result off screen? You can quickly scroll back with the flick of a finger. If you want to explore a function you graphed, you can use inertia scrolling and even pinch-zoom (and that speed comes in really handy here). Can you tell that I like this calculator? Even the freaking buttons are nicer than other calculators! AND it's cheaper than the nSpire. PRIME4LYFE,BTCHS!

#### VI. Vintage Scientific Calculators

Examples:

HP 15C,

HP 42S,

TI 68 I imagine you're all wondering why this category exists. To put it bluntly,

**these calculators are better than the current models** at many functions. I don't understand why, but the best scientific calculators seem to have been produced during the 80s and early 90s. All of these calculators are programmable. All of them handle matrices, and all of them can solve systems of complex-valued linear equations.

The

**HP 15c** is the oldest of these examples. It was recently brought back into production for a limited release in 2011. The release wasn't even that limited, but those calculators are now consistantly selling for ~$450. It is praised for it's horizontal layout, easy programmability, and excellent buttons.

The

**HP 42s** is the successor to the HP 41, and they are both widely considered to be the best scientific calculators of all time. Where the HP 41 had expansion ports for various peripherals, the HP 42s comes with much of that built in, and it comes in a much smaller package. There's no computer interface, but if you have the printer, you can use the IR port to print calculations and programs. I actually own one of these, and let me tell you, complex numbers are EXTREMELY well supported. Try calculating e

^{iπ} or ln(-1) on another calculator. You can even make complex matrices and store them in any of the numerous variables. Freaking awesome! The interface and display is also nicer than the 35s (it has soft-key-style menus). These calculators usually go for ~$200 on ebay. If you want to play around with a free version of this, have a look at

Free42 on iphone, android, linux, and windows.

The

**TI 68** is something I'm a little less familiar with. I do know it can solve systems of equations with up to 5 variables and even complex values. It's also keystroke programmable. I wouldn't mind getting my hands on one of these, but it's hard to find one that hasn't been half destroyed from use.

There are even older models than this, but when you start to look at calculators from the 1970s, you realize that certain features are missing (such as

continuous memory)

#### VII. Author's notes

I'm only a student, so I'm certainly not an expert on calculators, and there are many resources available all over the internet. Feel free to come over to

/calculators if you have any questions. There are a few of us who keep an eye on that sub, so questions usually get answered pretty quickly.

I plan on expanding this guide at some point in the future. If anyone has anything to add to this guide, please let me know, and I'll incorporate it (with credit). If there are any errors please

~~place them in the circular filing cabinet~~ let me know, and I'll make corrections. Any help is appreciated.

## Feel free to distribute this guide as you please so long as you include all of it. Remember to give me credit, and include this section and the additional credits section.

#### VIII. Change-log and Credits

None Yet

NOTE: slight wording changes and grammatical/spelling corrections may not be recorded

Hey guys does anyone have a torrent link or download link for the teacher version of the TI-Nspire™ CX CAS?