Category: Education

1.7 Numerical integration
As we have seen, the concept of integration is finding the accumulation of one variable multiplied by another (related) variable. In this section, we will explore the practical application of this concept to realworld data, where actual numerical values of variables are used to calculate accumulated sums. In industrial instrumentation, for example, we are often interested in…

1.6 Numerical differentiation in Calculus
As we have seen, the concept of differentiation is finding the rateofchange of one variable compared to another (related) variable. In this section, we will explore the practical application of this concept to realworld data, where actual numerical values of variables are used to calculate relative rates of change. In industrial instrumentation, for example, we are often…

1.5 Symbolic versus numerical calculus
Calculus has a reputation for being difficult to learn, and with good reason. The traditional approach to teaching calculus is based on manipulating symbols (variables) in equations, learning how different types of mathematical functions become transformed by the calculus operations of differentiation and integration. For example, suppose a firstsemester calculus student were given the following…

1.4 How derivatives and integrals relate to one another
First, let us review some of the properties of differentials and derivatives, referencing the expression and graph shown below: A differential is an infinitesimal increment of change (difference) in some continuouslychanging variable, represented either by a lowercase Roman letter d or a lowercase Greek letter “delta” (δ). Such a change in time would be represented as dt; a similar change in temperature as dT;…

1.3 The concept of integration in Calculus
Suppose we wished to measure the consumption of propane over time for a large propane storage tank supplying a building with heating fuel, because the tank lacked a level indicator to show how much fuel was left at any given time. The flow rate is sufficiently large, and the task sufficiently important, to justify the…

1.2 The concept of differentiation in Calculus
Suppose we wished to measure the rate of propane gas flow through a hose to a torch: Flowmeters appropriate for measuring low flow rates of any gas are typically very expensive, making it impractical to directly measure the flow rate of propane fuel gas consumed by this torch at any given moment. We could, however, indirectly measure…

1.1 Introduction to calculus
Few areas of mathematics are as powerfully useful in describing and analyzing the physical world as calculus: the mathematical study of changes. Calculus also happens to be tremendously confusing to most students first encountering it. A great deal of this confusion stems from mathematicians’ insistence on rigor1 and denial of intuition. Look around you right now. Do…

34.8 Helpful “tricks” using a digital multimeter (DMM)
The digital multimeter (DMM) is quite possibly the most useful tool in the instrument technician’s collection4 . This one piece of test equipment, properly wielded, yields valuable insight into the status and operation of many electrical and electronic systems. Not only is a goodquality multimeter capable of precisely indicating electrical voltage, current, and resistance, but it…

34.7 Common diagnostic mistakes
Volumes could be written about poor diagnostic technique. The following mistakes are not intended to comprise a comprehensive list, but are merely warnings against errors that are all too common among students and within the profession. 34.7.1 Failing to gather data Perhaps the most common mistake made by technicians attempting to diagnose a system problem is…

34.5 Problemsolving by simplification
A whole class of problemsolving techniques focuses on altering the given problem into a simpler form that is easier to analyze. Once a solution is found to the simplified problem, fresh ideas for attacking the original problem often become clear. This section will highlight multiple techniques for problemsimplification, as well as other useful techniques for problemsolving. The…

34.4 Mathematical problemsolving techniques
Some problemsolving techniques are unique to quantitative problems, involving mathematical calculations. In this section we will explore some useful tips to help you solve such problems. 34.4.1 Manipulating algebraic equations One of the most useful problemsolving techniques in all of algebra is the art of manipulating, or rewriting, equations to solve for a particular variable. The…

33.5 Policybased fortifications
These fortifications focus on human behavior rather than system design or component selection. In some ways these are the simplest to implement, as they generally require little in the way of technical expertise. This is not to suggest, however, that policybased fortifications are therefore the easiest to implement. On the contrary, changing human behavior is usually a…

33.4 Designbased fortifications
A designbased fortification is one rooted in technical details of system architecture and functionality. Some of these are quite simple (e.g. air gaps) while others are quite complex (e.g. encryption). In either case, these fortifications are ideally implemented at the inception of a new system, and at every point of system alteration or expansion. 33.4.1 Advanced authentication The…

33.3 Glossary of Cybersecurity Terms
Cybersecurity seems to have its own vocabulary, ranging from unwieldy technical acronyms to slang terms borrowed from amateur computer enthusiasts. What follows is a partial listing of some common terms and their definitions. This list is not only useful as a definitional reference when encountering such terms in cybersecurity literature, but it also serves to…

33.2 Motives for Compromising the Security of an Industrial Control System
There are multiple motives for compromising the security of an industrial control system, some of which overlap motives for attacking IT systems, and some of which are unique to the industrial world. This section details some of the reasons why people might wish to attack an industrial control system. 33.2.1 Technical challenge Computer experts tend to…