In the U.S. undergraduate engineering curricula, engineering economics is often a required course.^{[citation needed]} It is a topic on the Fundamentals of Engineering examination, and questions might also be asked on the Principles and Practice of Engineering examination; both are part of the Professional Engineering registration process.

Considering the time value of money is central to most engineering economic analyses. Cash flows are discounted using an interest rate, i, except in the most basic economic studies.

For each problem, there are usually many possible alternatives. One option that must be considered in each analysis, and is often the choice, is the do nothing alternative. The opportunity cost of making one choice over another must also be considered. There are also noneconomic factors to be considered, like color, style, public image, etc., and are called attributes.

Costs as well as revenues are considered, for each alternative, for an analysis period that is either a fixed number of years or the estimated life of the project. The salvage value is often forgotten, but is important, and is either the net cost or revenue for decommissioning the project.

Some other topics that may be addressed in engineering economics are inflation, uncertainty, replacements, depreciation, resource depletion, taxes, tax credits, accounting, cost estimations, or capital financing. All these topics are primary skills and knowledge areas in the field of cost engineering.

Since engineering is an important part of the manufacturing sector of the economy, engineering industrial economics is an important part of industrial or business economics. Major topics in engineering industrial economics are:

• the economics of the management, operation, and growth and profitability of engineering firms;

• macro-level engineering economic trends and issues;

• engineering product markets and demand influences; and

the development, marketing, and financing of new engineering technologies and products.

Basic Concepts:

Atom:

An atom is the basic unit of chemistry. It consists of a positively charged core, atomic nucleas, which contains protons and neutrons, and which maintains a number of electrons to balance the positive charge in the nucleus. The atom is also the smallest entity that can be envisaged to retain some of the of the element, such as electronegativity, ionization potential, preferred oxidation state(s), coordination number, and preferred types of bonds to form.

Elements and Periodic Table

The most convenient presentation of the chemical elements is in the periodic table of the chemical elements, which groups elements by atomic number. Due to its ingenious arrangement, groups, or columns, and periods or rows, of elements in the table either share several chemical properties, or follow a certain trend in characteristics such as atomic radius, electronegativity,  etc.

A Mole

A mole is the amount of a substance that contains as many elementary entities (atoms, molecules or ions) as there are atoms in 0.012 kilogram (or 12 grams) of carbon-12, where the carbon-12 atoms are unbound, at rest and in their ground state.^[37] This number is known as the Avogadro constant, and is determined empirically. The currently accepted value is 6.02214179(30) × 10²³ mol⁻¹ (2007 CODATA). The best way to understand the meaning of the term “mole” is to compare it to terms such as dozen. Just as one dozen is equal to 12, one mole is equal to 6.02214179(30) × 10²³. The term is used because it is much easier to say, for example, 1 mole of carbon atoms, than it is to say 6.02214179(30) × 10²³ carbon atoms. Likewise, we can describe the number of entities as a multiple or fraction of 1 mole, e.g. 2 mole or 0.5 moles. Mole is an absolute number (having no units) and can describe any type of elementary object, although the mole’s use is usually limited to measurement of subatomic, atomic, and molecular structures.

The number of moles of a substance in one liter of a solution is known as its molarity. Molarity is the common unit used to express the concentration of a solution in physical chemistry.

An ion is a charged species, an atom or a molecule, that has lost or gained one or more electrons. Positively charged cations (e.g. sodium cation Na⁺) and negatively charged anions (e.g. chloride Cl⁻) can form a crystalline lattice of neutral salts (e.g. sodium chloride NaCl). Examples of polyatomic ions that do not split up during acid-base reactions are hydroxide (OH⁻) and phosphate (PO₄³⁻).

Ions in the gaseous phase is often known as plasma.

Acidity or Alkalinity

A substance can often be classified as an acid or a base. This is often done on the basis of a particular kind of reaction, namely the exchange of protons between chemical compounds. However, an extension to this mode of classification was brewed up by the American chemist, Gilbert Newton Lewis; in this mode of classification the reaction is not limited to those occurring in an aqueous solution, thus is no longer limited to solutions in water. According to concept as per Lewis, the crucial things being exchanged are charges^[38]. There are several other ways in which a substance may be classified as an acid or a base, as is evident in the history of this concept ^[39]

In addition to the specific chemical properties that distinguish different chemical classifications chemicals can exist in several phases. For the most part, the chemical classifications are independent of these bulk phase classifications; however, some more exotic phases are incompatible with certain chemical properties. A phase is a set of states of a chemical system that have similar bulk structural properties, over a range of conditions, such as pressure or temperature. Physical properties, such as density and refractive index tend to fall within values characteristic of the phase. The phase of matter is defined by the phase transition, which is when energy put into or taken out of the system goes into rearranging the structure of the system, instead of changing the bulk conditions.

Sometimes the distinction between phases can be continuous instead of having a discrete boundary, in this case the matter is considered to be in a supercritical state. When three states meet based on the conditions, it is known as a triple point and since this is invariant, it is a convenient way to define a set of conditions.

The most familiar examples of phases are solids, liquids, and gases. Many substances exhibit multiple solid phases. For example, there are three phases of solid iron (alpha, gamma, and delta) that vary based on temperature and pressure. A principal difference between solid phases is the crystal structure, or arrangement, of the atoms. Another phase commonly encountered in the study of chemistry is the aqueous phase, whihch is the state of substances dissolved in aqueous solution (that is, in water). Less familiar phases include plasmas, Bose-Einstein condensates and fermionic condensates and the paramagnetic and ferromagnetic phases of magnetic materials. While most familiar phases deal with three-dimensional systems, it is also possible to define analogs in two-dimensional systems, which has received attention for its relevance to systems in biology.

Redox

It is a concept related to the ability of atoms of various substances to lose or gain electrons. Substances that have the ability to oxidize other substances are said to be oxidative and are known as oxidants or oxidizers. An oxidant removes electrons from another substance. Similarly, substances that have the ability to reduce other substances are said to be reductive and are known as reductants, or reducers. A reductant transfers electrons to another substance, and is thus oxidized itself. And because it “donates” electrons it is also called an electron donor. Oxidation and reduction properly refer to a change in oxidation number—the actual transfer of electrons may never occur. Thus, oxidation is better defined as an increase in oxidation number, and reduction as a decrease in oxidation number.

Bonding

Atoms sticking together in molecules or crystals are said to be bonded with one another. A chemical bond may be visualized as the multipole balance between the positive charges in the nuclei and the negative charges oscillating about them.^[40] More than simple attraction and repulsion, the energies and distributions characterize the availability of an electron to bond to another atom. These potentials create the interactions which hold atoms together in molecules or crystals. In many simple compounds, Valence Bond Theory, the Valence Shell Electron Pair Repulsion model (VSEPR), and the concept of oxidation number can be used to explain molecular structure and composition. Similarly, theories from classical physics can be used to predict many ionic structures. With more complicated compounds, such as metal complexes, valence bond theory fails and alternative approaches, primarily based on principles of quantum chemistry such as the molecular orbital theory, are necessary.

The IUPAC nomenclature of inorganic chemistry is a systematic method of naming inorganic chemical compounds as recommended by the International Union of Pure and Applied Chemistry (IUPAC). Ideally, every inorganic compound should have a name from which an unambiguous formula can be determined. There is also an IUPAC nomenclature of organic chemistry.

The names “caffeine” and “3,7-dihydro-1,3,7-trimethyl-1H-purine-2,6-dione” both signify the same chemical. The systematic name encodes the structure and composition of the caffeine molecule in some detail, and provides an unambiguous reference to this compound, whereas the name “caffeine” just names it. These advantages make the systematic name far superior to the common name when absolute clarity and precision are required. However, for the sake of brevity, even professional chemists will use the non-systematic name almost all of the time, because caffeine is a well-known common chemical with a unique structure. Similarly, H₂O is most often simply called water in English, though other chemical names do exist.

1. Single atom anions are named with an -ide suffix: for example, H⁻ is hydride.
2. Compounds with a positive ion (cation), the name of the compound is simply the cation’s name (usually the same as the element’s), followed by the anion. For example, NaCl is sodium chloride, and CaF₂ is calcium fluoride.
3. Cations able to take on more than one positive charge are labeled with Roman numerals in parentheses. For example, Cu⁺ is copper(I), Cu²⁺ is copper(II). An older, deprecated notation is to append -ous or -ic to the root of the Latin name to name ions with a lesser or greater charge. Under this naming convention, Cu⁺ is cuprous and Cu²⁺ is cupric. For naming metal complexes see the page on complex (chemistry).
4. Oxyanions (polyatomic anions containing oxygen) are named with -ite or -ate, for a lesser or greater quantity of oxygen. For example, NO₂⁻ is nitrite, while NO₃⁻ is nitrate. If four oxyanions are possible, the prefixes hypo- and per- are used: hypochlorite is ClO⁻, perchlorate is ClO₄⁻,
5. The prefix bi- is a deprecated way of indicating the presence of a single hydrogen ion, as in “sodium bicarbonate” (NaHCO₃). The modern method specifically names the hydrogen atom. Thus, NaHCO₃ would be pronounced “sodium hydrogen carbonate”.

Positively charged ions are called cations and negatively charged ions are called anions. The cation is always named first. Ions can be metals or polyatomic ions. Therefore the name of the metal or positive polyatomic ion is followed by the name of the non-metal or negative polyatomic ion. The positive ion retains its element name whereas for a single non-metal anion the ending is changed to -ide.

Example: sodium chloride, potassium oxide, or calcium carbonate.

When the metal has more than one possible ionic charge or oxidation number the name becomes ambiguous. In these cases the oxidation number of the metal ion is represented by a Roman numeral in parentheses immediately following the metal ion name. For example in uranium(VI) fluoride the oxidation number of uranium is 6. Another example is the iron oxides. FeO is iron(II) oxide and Fe₂O₃ is iron(III) oxide.

An older system used prefixes and suffixes to indicate the oxidation number, according to the following scheme:

Thus the four oxyacids of chlorine are called hypochlorous acid (HOCl), chlorous acid (HOClO), chloric acid (HOClO₂) and perchloric acid (HOClO₃), and their respective conjugate bases are the hypochlorite, chlorite, chlorate and perchlorate ions. This system has partially fallen out of use, but survives in the common names of many chemical compounds: the modern literature contains few references to “ferric chloride” (instead calling it “iron(III) chloride”), but names like “potassium permanganate” (instead of “potassium manganate(VII)”) and “sulfuric acid” abound.

Engineers priorities are welfare of society, law, profession, client, employer, other engineers and engineer himself (or herself).

NCEES Fundamentals of Engineering (FE) Examination ELECTRICAL EXAM SPECIFICATIONS Effective Beginning with the April 2009 Examinations
• The FE examination is an 8-hour supplied-reference examination: 120 questions in the 4-hour morning session and 60 questions in the 4-hour afternoon session.
• Examinees work all questions in the morning session and all questions in the afternoon module.
• The FE examination uses both the International System of Units (SI) and the US Customary System (USCS).
MORNING Session (120 questions in 12 topic areas)
Topic Area Approximate
Percentage of AM Test Content
I. Mathematics 15%

• A. Analytic geometry

• B. Integral calculus

• C. Matrix operations

• D. Roots of equations

• E. Vector analysis

• F. Differential equations

• G. Differential calculus

II. Engineering Probability and Statistics 7%

• A. Measures of central tendencies and dispersions (e.g., mean, mode, standard deviation)

• B. Probability distributions (e.g., discrete, continuous, normal, binomial)

• C. Conditional probabilities

• D. Estimation (e.g., point, confidence intervals) for a single mean

• E. Regression and curve fitting

• F. Expected value (weighted average) in decision-making

• G. Hypothesis testing

III. Chemistry 9%

• A. Nomenclature

• B. Oxidation and reduction

• C. Periodic table

• D. States of matter

• E. Acids and bases

• F. Equations (e.g., stoichiometry)

• G. Equilibrium

• H. Metals and nonmetals

IV. Computers 7%

• A. Terminology (e.g., memory types, CPU, baud rates, Internet)

• B. Spreadsheets (e.g., addresses, interpretation, “what if,” copying formulas)

• C. Structured programming (e.g., assignment statements, loops and branches, function calls)

V. Ethics and Business Practices 7%

• A. Code of ethics (professional and technical societies)

• B. Agreements and contracts

• C. Ethical versus legal

• D. Professional liability

• E. Public protection issues (e.g., licensing boards)

VI. Engineering Economics 8%

• A. Discounted cash flow (e.g., equivalence, PW, equivalent annual FW, rate of return)

• B. Cost (e.g., incremental, average, sunk, estimating)

• C. Analyses (e.g., breakeven, benefit-cost)

• D. Uncertainty (e.g., expected value and risk)

VII. Engineering Mechanics (Statics and Dynamics) 10%

• A. Statics
• Resultants of force systems

• Concurrent force systems

• Equilibrium of rigid bodies

• Frames and trusses

• Centroid of area

• 6. Area moments of inertia

• 7. Friction

• B. Dynamics

• Linear motion (e.g., force, mass, acceleration, momentum)

• Angular motion (e.g., torque, inertia, acceleration, momentum)

• Mass moments of inertia

• Impulse and momentum applications

• Work, energy, and power as applied to:

• Friction

VIII. Strength of Materials 7%

• A. Shear and moment diagrams
• B. Stress types (e.g., normal, shear, bending, torsion)
• C. Stress strain caused by:
• D. Deformations (e.g., axial, bending, torsion)
• E. Combined stresses
• F. Columns
• G. Indeterminant analysis
• H. Plastic versus elastic deformation

IX. Material Properties 7%

X. Fluid Mechanics 7%

• A. Flow measurement

• B. Fluid properties

• C. Fluid statics

• D. Energy, impulse, and momentum equations

• E. Pipe and other internal flow

XI. Electricity and Magnetism 9%

• A. Charge, energy, current, voltage, power

• B. Work done in moving a charge in an electric field (relationship between voltage and work)

• C. Force between charges

• D. Current and voltage laws (Kirchhoff, Ohm)

• E. Equivalent circuits (series, parallel)

• F. Capacitance and inductance

• G. Reactance and impedance, susceptance and admittance

• H. AC circuits

• I. Basic complex algebra

XII. Thermodynamics 7%

• A. Thermodynamic laws (e.g., 1st Law, 2nd Law)

• B. Energy, heat, and work

• C. Availability and reversibility

• D. Cycles

• E. Ideal gases

• F. Mixture of gases

• G. Phase changes

• H. Heat transfer

• I. Properties of:

AFTERNOON Session (60 questions in 9 topic areas)
Topic Area Approximate
Percentage of PM Test Content
I. Circuits 16%

• A. KCL, KVL

• B. Series/parallel equivalent circuits

• C. Node and loop analysis

• D. Thevenin/Norton theorems

• E. Impedance

• F. Transfer functions

• G. Frequency/transient response

• H. Resonance

• I. Laplace transforms

• J. 2-port theory

• K. Filters (simple passive)

II. Power 13%

• A. 3-phase

• B. Transmission lines

• C. Voltage regulation

• D. Delta and wye

• E. Phasors

• F. Motors

• G. Power electronics

• H. Power factor (pf)

• I. Transformers

III. Electromagnetics 7%

• A. Electrostatics/magnetostatics (e.g., measurement of spatial relationships, vector analysis)

• B. Wave propagation

• C. Transmission lines (high frequency)

IV. Control Systems 10%

• A. Block diagrams (feed forward, feedback)

• B. Bode plots

• C. Controller performance (gain, PID), steady-state errors

• D. Root locus

• E. Stability

V. Communications 9%

• A. Basic modulation/demodulation concepts (e.g., AM, FM, PCM)

• B. Fourier transforms/Fourier series

• C. Sampling theorem

• D. Computer networks, including OSI model

• E. Multiplexing

VI. Signal Processing 8%

• A. Analog/digital conversion

• B. Convolution (continuous and discrete)

• C. Difference equations

• D. Z-transforms

VII. Electronics 15%

• A. Solid-state fundamentals (tunneling, diffusion/drift current, energy bands, doping bands, p-n theory)

• B. Bias circuits

• C. Differential amplifiers

• D. Discrete devices (diodes, transistors, BJT, CMOS) and models and their performance

• E. Operational amplifiers

• F. Filters (active)

• G. Instrumentation (measurements, data acquisition, transducers)

VIII. Digital Systems 12%

• A. Numbering systems

• B. Data path/control system design

• C. Boolean logic

• D. Counters

• E. Flip-flops

• F. Programmable logic devices and gate arrays

• G. Logic gates and circuits

• H. Logic minimization (SOP, POS, Karnaugh maps)

• I. State tables/diagrams

• J. Timing diagrams

IX. Computer Systems 10%

• A. Architecture (e.g., pipelining, cache memory)

• B. Interfacing

• C. Microprocessors

• D. Memory technology and systems

• E. Software design methods (structured, top-down bottom-up, object-oriented design)

• F. Software implementation (structured programming, algorithms, data structures)

Fundamentals of Engineering (FE) Examination
Effective October 2005
• The FE examination is an 8-hour supplied-reference examination: 120 questions in the 4-hour morning
session and 60 questions in the 4-hour afternoon session.
• The afternoon session is administered in the following seven modules—Chemical, Civil, Electrical,
Environmental, Industrial, Mechanical, and Other/General engineering.
• Examinees work all questions in the morning session and all questions in the afternoon module they
have chosen.

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