engineering research

fe exam, electrical and computer test prep

ncees.org - info on test and signing up

- 110 questions, 6 hour with optional break. uses both SI and USCS units.

test topics

1. Mathematics (Questions: 11–17)
A. Algebra and trigonometry
B. Complex numbers
C. Discrete mathematics
D. Analytic geometry
E. Calculus (e.g., differential, integral, single-variable, multivariable)
F. Ordinary differential equations
G. Linear algebra
H. Vector analysis

2. Probability and Statistics (Questions: 4–6)
A. Measures of central tendencies and dispersions (e.g., mean, mode, standard deviation)
B. Probability distributions (e.g., discrete, continuous, normal, binomial, conditional probability)
C. Expected value (weighted average)

3. Ethics and Professional Practice (Questions: 4–6)
A. Codes of ethics (e.g., professional and technical societies, NCEES Model Law and Model Rules)
B. Intellectual property (e.g., copyright, trade secrets, patents, trademarks)
C. Safety (e.g., grounding, material safety data, PPE, radiation protection)

4. Engineering Economics (Questions: 5–8)
A. Time value of money (e.g., present value, future value, annuities)
B. Cost estimation
C. Risk identification
D. Analysis (e.g., cost-benefit, trade-off, break-even)

5. Properties of Electrical Materials (Questions: 4–6)
A. Semiconductor materials (e.g., tunneling, diffusion/drift current, energy bands, doping bands, p-n theory)
B. Electrical (e.g., conductivity, resistivity, permittivity, magnetic permeability, noise)
C. Thermal (e.g., conductivity, expansion)

6. Circuit Analysis (DC and AC Steady State) (Questions: 11–17)
A. KCL, KVL
B. Series/parallel equivalent circuits
C. Thevenin and Norton theorems
D. Node and loop analysis
E. Waveform analysis (e.g., RMS, average, frequency, phase, wavelength)
F. Phasors
G. Impedance

7. Linear Systems (Questions: 5–8)
A. Frequency/transient response
B. Resonance
C. Laplace transforms
D. Transfer functions

8. Signal Processing (Questions: 5–8)
A. Sampling (e.g., aliasing, Nyquist theorem)
B. Analog filters
C. Digital filters (e.g., difference equations, Z-transforms)

9. Electronics (Questions: 7–11)
A. Models, biasing, and performance of discrete devices (e.g., diodes, transistors, thyristors)
B. Amplifiers (e.g., single-stage/common emitter, differential, biasing)
C. Operational amplifiers (e.g., ideal, nonideal)
D. Instrumentation (e.g., measurements, data acquisition, transducers)
E. Power electronics (e.g., rectifiers, inverters, converters)

10. Power Systems (Questions: 8–12)
A. Power theory (e.g., power factor, single and three phase, voltage regulation)
B. Transmission and distribution (e.g., real and reactive losses, efficiency, voltage drop, delta and wye connections)
C. Transformers (e.g., single-phase and three-phase connections, reflected impedance)
D. Motors and generators (e.g., synchronous, induction, dc)

11. Electromagnetics (Questions: 4–6)
A. Electrostatics/magnetostatics (e.g., spatial relationships, vector analysis)
B. Electrodynamics (e.g., Maxwell equations, wave propagation)
C. Transmission lines (high frequency)

12. Control Systems (Questions: 6–9)
A. Block diagrams (e.g. feedforward, feedback)
B. Bode plots
C. Closed-loop response, open-loop response, and stability
D. Controller performance (e.g., steady-state errors, settling time, overshoot)

13. Communications (Questions: 5–8)
A. Basic modulation/demodulation concepts (e.g., AM, FM, PCM)
B. Fourier transforms/Fourier series
C. Multiplexing (e.g., time division, frequency division, code division)
D. Digital communications

14. Computer Networks (Questions: 4–6)
A. Routing and switching
B. Network topologies (e.g., mesh, ring, star)
C. Network types (e.g., LAN, WAN, internet)
D. Network models (e.g., OSI, TCP/IP)
E. Network intrusion detection and prevention (e.g., firewalls, endpoint detection, network detection)
F. Security (e.g., port scanning, network vulnerability testing, web vulnerability testing, penetration testing, security triad)

15. Digital Systems (Questions: 8–12)
A. Number systems
B. Boolean logic
C. Logic gates and circuits
D. Logic minimization (e.g., SOP, POS, Karnaugh maps)
E. Flip-flops and counters
F. Programmable logic devices and gate arrays
G. State machine design
H. Timing (e.g., diagrams, asynchronous inputs, race conditions and other hazards)

16. Computer Systems (Questions: 5–8)
A. Microprocessors
B. Memory technology and systems
C. Interfacing

17. Software Engineering (Questions: 4–6)
A. Algorithms (e.g., sorting, searching, complexity, big-O)
B. Data structures (e.g., lists, trees, vectors, structures, arrays)
C. Software implementation (e.g., iteration, conditionals, recursion, control flow, scripting, testing)

links

• ncees.org - info on test and signing up
• FE Electrical and Computer Topics - pdf of topics for the exam

wikis

• Navier Stokes equations
• Dynamic link library
• Polymorphism(computer science)
• Polymorphic code

fe notes

14. Computer Networks (4-6) ibm - networking ibm - network security A. Routing and Switching
tba

B. Network Topologies
(mesh, ring, star)

While architecture represents the theoretical framework of a network, topology is the practical implementation of the architectural framework. Network topology describes the physical and logical arrangement of nodes and links on a network, including all hardware (routers, switches, cables), software (apps and operating systems) and transmission media (wired or wireless connections).

Bus network topology: every network node is directly connected to a main cable.

Ring topology: nodes are connected in a loop, so each device has exactly two neighbors. Adjacent pairs are connected directly and nonadjacent pairs are connected indirectly through intermediary nodes.

Star network topologies: has a single, central hub through which all nodes are indirectly connected.

Mesh topologies are overlapping connections between nodes. There are two types of mesh networks—full mesh and partial mesh.

In a full mesh topology, every network node connects to every other network node, providing the highest level of network resilience. In a partial mesh topology, only some network nodes connect, typically those that exchange data most frequently.

Full mesh topologies can be expensive and time-consuming to run, normally reserved for networks that require high redundancy. Partial mesh, on the other hand, provides less redundancy but is more cost-effective and simpler to run.

C. Network Types
(LAN, WAN, internet)
Types by geographical area
Local area network (LAN)
A LAN connects computers over a relatively short distance, such as those within an office building, school or hospital. LANs are typically privately owned and managed.
Wide area network (WAN)
As the name implies, a WAN connects computers across large geographical areas, such as regions and continents. WANs often have collective or distributed ownership models for network management purposes. Cloud networks serve as one example, since they’re hosted and delivered by public and private cloud infrastructures across the globe.
A software-defined wide area network (SD-WAN) is a virtualized WAN architecture that uses SDN principles to centralize the management of disconnected WAN networks and optimize network performance.
Metropolitan area network (MAN)
MANs are larger than LANs but smaller than WANs. Cities and government entities typically own and manage MANs.
Personal area network (PAN)
A PAN serves one person. If a user has multiple devices from the same manufacturer (an iPhone and a MacBook, for instance), it’s likely they've set up a PAN that shares and syncs content—text messages, emails, photos and more—across devices.

Types by transmission medium
Wired networks
Wired network devices are connected by physical wires and cables, including copper wires and Ethernet, twisted pair, coaxial or fiber optic cables. Network size and speed requirements typically dictate the choice of cable, the arrangement of network elements and the physical distance between devices.
Wireless networks
Wireless networks forgo cables for infrared, radio or electromagnetic wave transmission across wireless devices with built-in antennae and sensors.

Types by communication type
Multipoint networks
In a multipoint network, multiple devices share channel capacity and network links.
Point-to-point networks
Network devices establish a direct node-to-node link to transmit data.
Broadcast networks
On broadcast networks, several interested “parties” (devices) can receive one-way transmissions from a single sending device. Television stations are a great example of broadcast networks.
Virtual private networks (VPNs)
A VPN is a secure, point-to-point connection between two network endpoints. It establishes an encrypted channel that keeps a user’s identity and access credentials, as well as any data transferred, inaccessible to hackers.
D. Network Models
(OSI, TCP/IP)
Transmission Control Protocol (TCP) is a communications standard that enables application programs and computing devices to exchange messages over a network. It is designed to send packets across the internet and ensure the successful delivery of data and messages over networks.
Many modern networks run on TCP/IP models, which include four network layers.
Network access layer. Also called the data link layer or the physical layer, the network access layer of a TCP/IP network includes the network infrastructure (hardware and software components) necessary for interfacing with the network medium. It handles physical data transmission—using Ethernet and protocols such as the address resolution protocol (ARP)—between devices on the same network.
Internet layer.
The internet layer is responsible for logical addressing, routing and packet forwarding. It primarily relies on the IP protocol and the Internet Control Message Protocol (ICMP), which manages addressing and routing of packets across different networks.
Transport layer. The TCP/IP transport layer enables data transfer between upper and lower layers of the network. Using TCP and UDP protocols, it also provides mechanisms for error checking and flow control.
TCP is a connection-based protocol that is generally slower but more reliable than UDP. UDP is a connectionless protocol that is faster than TCP but does not provide guaranteed transfer. UDP protocols facilitate packet transmission for time-sensitive apps (such as video streaming and gaming platforms) and DNS lookups.
Application layer. TCP/IP’s application layer uses HTTP, FTP, Post Office Protocol 3 (POP3), SMTP, domain name system (DNS) and SSH protocols to provide network services directly to applications. It also manages all the protocols that support user applications.
Though TCP/IP is more directly applicable to networking, the Open Systems Interconnection (OSI) model has also had a substantial impact on computer networking and computer science, writ broadly.
OSI is a conceptual model that divides network communication into seven abstract layers (instead of four), providing a theoretical underpinning that helps engineers and developers understand the intricacies of network communication. The OSI model's primary value lies in its educational utility and its role as a conceptual framework for designing new protocols, making sure that they can interoperate with existing systems and technologies.
However, the TCP/IP model's practical focus and real-world applicability have made it the backbone of modern networking. Its robust, scalable design and horizontal layering approach has driven the explosive growth of the internet, accommodating billions of devices and massive amounts of data traffic.

E. Network Intrusion, Detection, Prevention
(firewalls, endpoint detection, network detection)
Firewalls
A firewall is software or hardware that stops suspicious traffic from entering or leaving a network while letting legitimate traffic through. Firewalls can be deployed at the edges of a network or used internally to divide a larger network into smaller subnetworks. If one part of the network is compromised, hackers are still shut off from the rest.
There are different types of firewalls with different features. Basic firewalls use packet filtering to inspect traffic. More advanced next-generation firewalls add intrusion prevention, AI and machine learning, application awareness and control, and threat intelligence feeds for extra protection.
Network access control (NAC)
Network access control solutions act like gatekeepers, authenticating and authorizing users to determine who is allowed into the network and what they can do inside. "Authentication" means verifying that a user is who they claim to be. It also means granting authenticated users permission to access network resources.
NAC solutions are often used to enforce role-based access control (RBAC) policies, in which users' privileges are based on their job functions. For example, a junior developer might be able to view and edit code but not push it live. In contrast, senior developers could read, write and push code to production. RBAC helps prevent data breaches by keeping unauthorized users away from assets they are not permitted to access.
In addition to authenticating users, some NAC solutions can do risk assessments on users' endpoints. The goal is to keep unsecured or compromised devices from accessing the network. If a user tries to enter the network on a device with outdated anti-malware software or incorrect configurations, the NAC will deny access. Some advanced NAC tools can automatically fix non-compliant endpoints.
Intrusion detection and prevention systems (IDPSs)
An intrusion detection and prevention system—sometimes called an intrusion prevention system—can be deployed directly behind a firewall to scan incoming traffic for security threats. These security tools evolved from intrusion detection systems, which only flagged suspicious activity for review. IDPSs have the added ability to automatically respond to possible breaches, such as by blocking traffic or resetting the connection. IDPSs are particularly effective at detecting and blocking brute force attacks and denial of service (DoS) or distributed denial of service (DDoS) attacks.
Virtual private networks (VPNs)
A virtual private network (VPN) protects a user's identity by encrypting their data and masking their IP address and location. When someone uses a VPN, they no longer connect directly to the internet but to a secure server that connects to the internet on their behalf.
VPNs can help remote workers securely access corporate networks, even through unsecured public wifi connections like those found in coffee shops and airports. VPNs encrypt a user's traffic, keeping it safe from hackers who might want to intercept their communications.
Instead of VPNs, some organizations use zero trust network access (ZTNA). Rather than using a proxy server, ZTNA uses zero trust access control policies to securely connect remote users. When remote users log in to a network through ZTNA, they don't gain access to the whole network. Instead, they only gain access to the specific assets they're permitted to use, and they must be reverified every time they access a new resource.
Application security
Application security refers to the steps security teams take to protect apps and application programming interfaces (APIs) from network attackers. Because many companies today use apps to carry out key business functions or process sensitive data, apps are a common target for cybercriminals. And because so many business apps are hosted in public clouds, hackers can exploit their vulnerabilities to break into private company networks.
Application security measures defend apps from malicious actors. Common application security tools include web application firewalls, runtime application self-protection, static application security testing and dynamic application security testing.
Email security
The IBM X-Force® Threat Intelligence Index found that phishing is the most common initial cyberattack vector. Email security tools can help thwart phishing attacks and other attempts to compromise users' email accounts. Most email services have built-in security tools like spam filters and message encryption. Some email security tools feature sandboxes, isolated environments where security teams can inspect email attachments for malware without exposing the network.
Data loss prevention (DLP)
Data loss prevention refers to information security strategies and tools that ensure sensitive data is neither stolen nor accidentally leaked. DLP includes data security policies and purpose-built technologies that track data flows, encrypt sensitive information and raise alerts when suspicious activity is detected.
Endpoint security
Endpoint security solutions protect any devices that connect to a network—such as laptops, desktops, servers, mobile devices or IoT devices—against hackers who try to use them to sneak into the network. Antivirus software can detect and destroy trojans, spyware, and other malicious software on a device before it spreads to the rest of the network.
Endpoint detection and response solutions are more advanced tools that monitor endpoint behavior and automatically respond to security events. Unified endpoint management software allows companies to monitor, manage and secure all end-user devices from a single console.
Web security
Web security solutions, such as secure web gateways, block malicious internet traffic and keep users from connecting to suspicious websites and apps.
Network segmentation
Network segmentation is a way of breaking large networks down into smaller subnetworks, either physically or through software. Network segmentation can limit the spread of ransomware and other malware by walling off a compromised subnetwork from the rest of the network. Segmentation can also help keep legitimate users away from assets they shouldn't access.
Cloud security
Cloud security solutions protect data centers, apps and other cloud assets from cyberattacks. Most cloud security solutions are simply standard network security measures—such as firewalls, NACs, and VPNs—applied to cloud environments. Many cloud service providers build security controls into their services or offer them as add-ons.
User and entity behavior analytics (UEBA)
User and entity behavior analytics uses behavioral analytics and machine learning to flag abnormal user and device activity. UEBA can help catch insider threats and hackers who have hijacked user accounts.
F. Security
(port scanning, network vulnerability testing, web vulnerability testing, penetration testing, security triad)
While a defense-in-depth approach can protect a company's network, it also means the IT security team has to manage a number of separate security controls. Enterprise network security platforms can help streamline network security management by integrating disparate security tools and allowing security teams to monitor the whole network from a single console. Common network security platforms include:
Security information and event management (SIEM)
Security orchestration, automation and response (SOAR)
Network detection and response (NDR)
Extended detection and response (XDR)
Security information and event management collects information from internal security tools, aggregates it in a central log and flags anomalies.
Security orchestration, automation and response solutions collect and analyze security data and allow security teams to define and execute automated responses to cyberthreats.
Network detection and response tools use AI and machine learning to monitor network traffic and detect suspicious activity.
Extended detection and response is an open cybersecurity architecture that integrates security tools and unifies security operations across all security layers—users, endpoints, email, applications, networks, cloud workloads and data. With XDR, security solutions that aren’t necessarily designed to work together can interoperate seamlessly on threat prevention, detection, investigation and response. XDR can also automate threat detection, incident triage and threat hunting workflows.

16. Computer Systems (5-8)
A. Microprocessors
A microprocessor is a single semiconductor chip that integrates the main five functional units of a computer: arithmetic/logical, control, storage, input, and output. It serves as the “superintendent,” or central processing unit (CPU), of the computer.
tel - microprocessor A semiconductor is a material with electrical conductivity between that of a conductor and an insulator.[1] Its conductivity can be modified by adding impurities ("doping") to its crystal structure. When two regions with different doping levels are present in the same crystal, they form a semiconductor junction.
Semiconductor Microcontroller units (MCUs) and microprocessor units (MPUs) are two kinds of integrated circuits that, while similar in certain ways, are very different in many others. Replacing antiquated multi-component central processing units (CPUs) with separate logic units, these single-chip processors are both extremely valuable in the continued development of computing technology. However, microcontrollers and microprocessors differ significantly in component structure, chip architecture, performance capabilities and application.
The key difference between these two units is that microcontrollers combine all the necessary elements of a microcomputer system onto a single piece of hardware. Microcontrollers do not require additional peripherals or complex operating systems to function, while microprocessors do. Both circuits contain CPUs, however, microcontrollers also integrate memory, input/output (I/O) components and other varied peripherals.
ibm - microcontroller vs microprocessor B. Memory technology and systems
Memory is what your computer uses to store data temporarily, while storage is where you save files permanently.
When you save a file, it's copied from the memory onto the storage drive. This is why your computer seems to run slower when it's low on memory; it has to pull data from the storage drive in order to use it. To free up some memory, try closing unused applications or deleting temporary files.

various notes

- The Navier–Stokes equations are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes).
- The Navier–Stokes equations mathematically express momentum balance for Newtonian fluids and make use of conservation of mass. They are sometimes accompanied by an equation of state relating pressure, temperature and density. They arise from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing viscous flow. The difference between them and the closely related Euler equations is that Navier–Stokes equations take viscosity into account while the Euler equations model only inviscid flow. As a result, the Navier–Stokes are a parabolic equation and therefore have better analytic properties, at the expense of having less mathematical structure (e.g. they are never completely integrable). - Point of inflection
- Inflection points are points where the function changes concavity, i.e. from being "concave up" to being "concave down" or vice versa. Points of inflection can occur where the second derivative is zero. In other words, solve for f" = 0
- In condensed matter physics and materials science, an amorphous or non-crystalline solid is a solid that lacks the long-range order that is characteristic of a crystal.
- An integrated circuit (IC), also known as a microchip or simply chip, is a set of electronic circuits, consisting of various electronic components (such as transistors, resistors, and capacitors) and their interconnections. These components are etched onto a small, flat piece ("chip") of semiconductor material, usually silicon. Integrated circuits are used in a wide range of electronic devices, including computers, smartphones, and televisions, to perform various functions such as processing and storing information. They have greatly impacted the field of electronics by enabling device miniaturization and enhanced functionality.

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