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From “A Brief History of the Calculator” by Natalia Koval and Max Whitacre:

The mechanical calculator was limited, at first, to addition and subtraction. Later models incorporated multiplication and division. However, they were somewhat difficult to operate and slow. They were also constrained by the precision (the number of the decimal places before and after the decimal point) that they produced, but the answers were accurate. Given these limitations, the mechanical calculator was used for only the most basic of computations in engineering.

The electronic calculator resolved the problems of the slide ruler and mechanical calculator and was a great boon to engineers. The electronic calculator also allowed for greater mathematical operations, and later for simple programming operations. They still had a limitation on precision (based on the circuitry used to perform the calculation) but they had much greater precision than a slide ruler or mechanical calculator. As a result, engineers could now design for smaller tolerances, which reduced the size and weight, led to greater efficiencies, and reduced the costs of the product. More information can be found on the Wikipedia Article on Calculators.

Computers

Mainframe Computers	Mainframe computers (colloquially referred to as "big iron") are computers used primarily by large organizations for critical applications, bulk data processing, such as census, industry and consumer statistics, enterprise resource planning, and transaction processing. The term originally referred to the large cabinets called "main frames" that housed the central processing unit and main memory of early computers. Later, the term was used to distinguish high-end commercial machines from less powerful units. Most large-scale computer system architectures were established in the 1960s but continue to evolve. The initial manufactures of mainframe computers were IBM, Burroughs, Univac, Sperry-Rand, and GE.
Minicomputers	A minicomputer, or colloquially mini, is a class of smaller computers that was developed in the mid-1960s and sold for much less than mainframe and mid-size computers from IBM and its direct competitors. In a 1970 survey, the New York Times suggested a consensus definition of a minicomputer as a machine costing less than US$25,000, with an input-output device such as a teleprinter and at least four thousand words of memory, that is capable of running programs in a higher-level language, such as Fortran or BASIC. The class formed a distinct group with its own software architectures and operating systems. Minis were designed for control, instrumentation, human interaction, and communication switching as distinct from calculation and record keeping. Many were sold indirectly to original equipment manufacturers (OEMs) for final end use application. During the two-decade lifetime of the minicomputer class (1965–1985), almost 100 companies formed and only a half dozen remained. When single-chip CPU microprocessors appeared, beginning with the Intel 4004 in 1971, the term "minicomputer" came to mean a machine that lies in the middle range of the computing spectrum, in between the smallest mainframe computers and the microcomputers. The term "minicomputer" is little used today; the contemporary term for this class of system is "midrange computer", such as the higher-end SPARC, Power Architecture and Itanium-based systems from Oracle, IBM and Hewlett-Packard. The initial manufactures of minicomputers were Digital Equipment Corporation (DEC), Data General, Prime, Computervision, Honeywell and Wang Laboratories
Workstation Computers	A workstation is a special computer designed for technical or scientific applications. Intended primarily to be used by one person at a time, they are commonly connected to a local area network and run multi-user operating systems. The term workstation has also been used loosely to refer to everything from a mainframe computer terminal to a PC connected to a network, but the most common form refers to the group of hardware offered by several current and defunct companies such as Sun Microsystems, Silicon Graphics, Apollo Computer, DEC, HP, NeXT and IBM which opened the door for the 3D graphics animation revolution of the late 1990s. Workstations offered higher performance than mainstream personal computers, especially with respect to CPU and graphics, memory capacity, and multitasking capability. Workstations were optimized for the visualization and manipulation of different types of complex data such as 3D mechanical design, engineering simulation (e.g., computational fluid dynamics), animation and rendering of images, and mathematical plots. Typically, the form factor is that of a desktop computer, consist of a high-resolution display, a keyboard and a mouse at a minimum, but also offer multiple displays, graphics tablets, 3D mice (devices for manipulating 3D objects and navigating scenes), etc. Workstations were the first segment of the computer market to present advanced accessories and collaboration tools. The increasing capabilities of mainstream PCs in the late 1990s have blurred the lines somewhat with technical/scientific workstations.  The workstation market previously employed proprietary hardware which made them distinct from PCs; for instance, IBM used RISC-based CPUs for its workstations and Intel x86 CPUs for its business/consumer PCs during the 1990s and 2000s. However, by the early 2000s this difference disappeared, as workstations now use highly commoditized hardware dominated by large PC vendors, such as Dell, Hewlett-Packard (later HP Inc.) and Fujitsu, selling Microsoft Windows or Linux systems running on x86-64 architecture such as Intel Xeon or AMD Opteron CPU Microcomputers 1980 to present.
Microcomputers	The first microcomputer was the Japanese Sord Computer Corporation's SMP80/08 (1972), which was followed by the SMP80/x (1974). The French developers of the Micral N (1973) filed their patents with the term "Micro-ordinateur", a literal equivalent of "Microcomputer", to designate a solid-state machine designed with a microprocessor. In the USA, the earliest models such as the Altair 8800 and Apple I were often sold as kits to be assembled by the user, and came with as little as 256 bytes of RAM, and no input/output devices other than indicator lights and switches, useful as a proof of concept to demonstrate what such a simple device could do. However, as microprocessors and semiconductor memory became less expensive, microcomputers in turn grew cheaper and easier to use. All these improvements in cost and usability resulted in an explosion in their popularity during the late 1970s and early 1980s. A large number of computer makers packaged microcomputers for use in small business applications. By 1979, many companies such as Cromemco, Processor Technology, IMSAI, North Star Computers, Southwest Technical Products Corporation, Ohio Scientific, Altos Computer Systems, Morrow Designs and others produced systems designed either for a resourceful end user or consulting firm to deliver business systems such as accounting, database management, and word processing to small businesses. This allowed businesses unable to afford leasing of a minicomputer or time-sharing service the opportunity to automate business functions, without (usually) hiring a full-time staff to operate the computers. A representative system of this era would have used an S100 bus, an 8-bit processor such as an Intel 8080 or Zilog Z80, and either CP/M or MP/M operating system. The increasing availability and power of desktop computers for personal use attracted the attention of more software developers. In time, and as the industry matured, the market for personal computers standardized around IBM PC compatibles running DOS, and later Windows. Modern desktop computers, video game consoles, laptops, tablet PCs, and many types of handheld devices, including mobile phones, pocket calculators, and industrial embedded systems, may all be considered examples of microcomputers according to the definition given above. The initial manufactures of microcomputers that gained wide acceptance were Apple, Radio Shack, Commodore, Osborne, and Kaypro. The later manufactures of microcomputers were Apple, IBM, Compaq, Dell Computer, Packard Bell, AST Research, and Gateway 2000. Today there are literally dozens of manufactures of microcomputers.
Supercomputers	A supercomputer is a computer with a high level of computing performance compared to a general-purpose computer. Performance of a supercomputer is measured in floating-point operations per second (FLOPS) instead of million instructions per second (MIPS). As of 2015, there are supercomputers which can perform up to quadrillions of FLOPS, measured in P(eta)FLOPS. The majority of supercomputers today run Linux-based operating systems. Supercomputers play an important role in the field of computational science, and are used for a wide range of computationally intensive tasks in various fields, including quantum mechanics, weather forecasting, climate research, oil and gas exploration, molecular modeling (computing the structures and properties of chemical compounds, biological macromolecules, polymers, and crystals), and physical simulations (such as simulations of the early moments of the universe, airplane and spacecraft aerodynamics, the detonation of nuclear weapons, and nuclear fusion). Throughout their history, they have been essential in the field of cryptanalysis. Supercomputers were introduced in the 1960s, and for several decades the fastest were made by Seymour Cray at Control Data Corporation (CDC), Cray Research and subsequent companies bearing his name or monogram. The first such machines were highly tuned conventional designs that ran faster than their more general-purpose contemporaries. Through the 1960s, they began to add increasing amounts of parallelism with one to four processors being typical. From the 1970s, the vector computing concept with specialized math units operating on large arrays of data came to dominate. A notable example is the highly successful Cray-1 of 1976. Vector computers remained the dominant design into the 1990s. From then until today, massively parallel supercomputers with tens of thousands of off-the-shelf processors became the norm.

The computer had a tremendous impact on engineering, as it resolved all the issues of the slide ruler, mechanical calculator, and the electronic calculator. In addition, it had a full array of mathematical operations, with much greater precision, and was fully programmable for complex calculations. As computers became faster, smaller, and less expensive they were integrated into engineering at all levels. They even spawned the development of Computer Aided Design (CAD), Computer Aided Engineering (CAE), and Computer Aided Manufacturing (CAM) software applications. The subject of Computer Modeling and its Issues, Concerns, and Limitations is another paper that I have written and is beyond the scope of this paper. I would direct you to this paper “Computer Modeling” for further information. Below is the recap of this paper.

Conclusions

Mathematical Tools are like any other tool - they can be used properly or improperly, by a skilled or unskilled persons, and even if used properly in the hands of a skilled person they can produce improper or incorrect results. When used in the hands of of a biased person they can give the false illusion of correctness and believably of the results, as I have examined in another article of mine, Oh What a Tangled Web We Weave. Consequently, we should all be wary of Mathematical Tools results, and verify to the best of our ability their correctness before we proceed with the results. We should also remember that there are things that we know, things that we know we don't know, and things that we don't know that we don't know—and it is the things that we don't know that we don't know where the serious problems often arise.

Disclaimer

Please Note - many academics, scientist and engineers would critique what I have written here as not accurate nor through. I freely acknowledge that these critiques are correct. It was not my intentions to be accurate or through, as I am not qualified to give an accurate nor through description. My intention was to be understandable to a layperson so that they can grasp the concepts. Academics, scientists, and engineers entire education and training is based on accuracy and thoroughness, and as such, they strive for this accuracy and thoroughness. I believe it is essential for all laypersons to grasp the concepts of this paper, so they make more informed decisions on those areas of human endeavors that deal with this subject. As such, I did not strive for accuracy and thoroughness, only understandability.

Most academics, scientist, and engineers when speaking or writing for the general public (and many science writers as well) strive to be understandable to the general public. However, they often fall short on the understandability because of their commitment to accuracy and thoroughness, as well as some audience awareness factors. Their two biggest problems are accuracy and the audience knowledge of the topic.

Accuracy is a problem because academics, scientist, engineers and science writers are loath to be inaccurate. This is because they want the audience to obtain the correct information, and the possible negative repercussions amongst their colleagues and the scientific community at large if they are inaccurate. However, because modern science is complex this accuracy can, and often, leads to confusion amongst the audience.

The audience knowledge of the topic is important as most modern science is complex, with its own words, terminology, and basic concepts the audience is unfamiliar with, or they misinterpret. The audience becomes confused (even while smiling and lauding the academics, scientists, engineers or science writer), and the audience does not achieve understandability. Many times, the academics, scientists, engineers or science writer utilizes the scientific disciplines own words, terminology, and basic concepts without realizing the audience misinterpretations, or has no comprehension of these items.

It is for this reason that I place understandability as the highest priority in my writing, and I am willing to sacrifice accuracy and thoroughness to achieve understandability. There are many books, websites, and videos available that are more accurate and through. The subchapter on “Further Readings” also contains books on various subjects that can provide more accurate and thorough information. I leave it to the reader to decide if they want more accurate or through information and to seek out these books, websites, and videos for this information.