Fundamentals of Engineering Exam Review

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About this course: The purpose of this course is to review the material covered in the Fundamentals of Engineering (FE) exam to enable the student to pass it. It will be presented in modules corresponding to the FE topics, particularly those in Civil and Mechanical Engineering. Each module will review main concepts, illustrate them with examples, and provide extensive practice problems.

Created by:  Georgia Institute of Technology
  • Taught by:  Dr. Philip Roberts, Professor

    School of Civil and Environmental Engineering
Language English How To Pass Pass all graded assignments to complete the course. User Ratings 4.7 stars Average User Rating 4.7See what…

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When you enroll for courses through Coursera you get to choose for a paid plan or for a free plan

  • Free plan: No certicification and/or audit only. You will have access to all course materials except graded items.
  • Paid plan: Commit to earning a Certificate—it's a trusted, shareable way to showcase your new skills.

About this course: The purpose of this course is to review the material covered in the Fundamentals of Engineering (FE) exam to enable the student to pass it. It will be presented in modules corresponding to the FE topics, particularly those in Civil and Mechanical Engineering. Each module will review main concepts, illustrate them with examples, and provide extensive practice problems.

Created by:  Georgia Institute of Technology
  • Taught by:  Dr. Philip Roberts, Professor

    School of Civil and Environmental Engineering
Language English How To Pass Pass all graded assignments to complete the course. User Ratings 4.7 stars Average User Rating 4.7See what learners said Coursework

Each course is like an interactive textbook, featuring pre-recorded videos, quizzes and projects.

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Georgia Institute of Technology The Georgia Institute of Technology is one of the nation's top research universities, distinguished by its commitment to improving the human condition through advanced science and technology. Georgia Tech's campus occupies 400 acres in the heart of the city of Atlanta, where more than 20,000 undergraduate and graduate students receive a focused, technologically based education.

Syllabus


WEEK 1


ABOUT THIS COURSE
This section of the course will provide you with an overview of the course, an outline of the topics covered, as well as instructor comments about the Fundamentals of Engineering Exam and reference handbook.


3 videos, 3 readings expand


  1. Video: Welcome!
  2. Reading: Course Syllabus
  3. Reading: Consent Form
  4. Video: Overview comments
  5. Video: Reference Handbook
  6. Reading: Get from Georgia Tech


WEEK 2


Mathematics



This module reviews the basic principles of mathematics covered in the FE Exam. We first review the equations and characteristics of straight lines, then classify polynomial equations, define quadric surfaces and conics, and trigonometric identities and areas. In algebra we define complex numbers and logarithms, and show how to manipulate matrices and determinants. Basic properties of vectors with their manipulations and identities are presented. The discussion of series includes arithmetic and geometric progressions and Taylor and Maclaurin series. Calculus begins with definitions of derivatives and gives some standard forms and computation of critical points of curves, then presents grad, del and curl operators on scalar and vector functions. Differential equations are calcified and to methods to solve linear, homogenous equations are presented. Fourier series and transforms are defined along with standard forms, and finally Laplace transforms and their inverse are discussed. In all cases, basic ideas and equations are presented along with sample problems that illustrate the major ideas and provide practice on expected exam questions.Time: Approximately 4.5 hours | Difficulty Level: Medium


15 videos, 2 readings expand


  1. Reading: Learning Objectives
  2. Video: Analytic Geometry and Trigonometry: Straight Lines
  3. Video: Analytic Geometry and Trigonometry: Polynomials and Conics
  4. Video: Analytic and Geometry and Trigonometry: Trigonometry
  5. Video: Algebra and Linear Algebra: Complex numbers and logarithms
  6. Video: Algebra and Linear Algebra: Matrices and determinants
  7. Video: Vectors: Basic Definitions and operations
  8. Video: Vectors: Examples
  9. Video: Series: Arithmetic and geometric progressions
  10. Video: Calculus: Derivatives and curvature
  11. Video: Calculus: Integration
  12. Video: Calculus: Gradient, divergence and curl
  13. Video: DifferentialEq: Classification
  14. Video: DifferentialEq: Solutions
  15. Video: DifferentialEq: Fourier series
  16. Video: DifferentialEq: Laplace
  17. Reading: Earn a Georgia Tech Badge/Certificate/CEUs

Graded: Mathematics Supplemental Questions

WEEK 3


Probability and Statistics



This module reviews the basic principles of probability and statistics covered in the FE Exam. We first review some basic parameters and definitions in statistics, such as mean and dispersion properties followed by computation of permutations and combinations. We then give the definitions of probability and the laws governing it and apply Bayes theorem. We study probability distributions and cumulative functions, and learn how to compute an expected value. Particular probability distributions covered are the binomial distribution, applied to discrete binary events, and the normal, or Gaussian, distribution. We show the meaning of confidence levels and intervals and how to use and apply them. We define and apply the central limit theorem to sampling problems and brieflyt- and c2. We define hypothesis testing and show how to apply it to random data. Finally, we show how to apply linear regression estimates to data and estimate the degree of fit including correlation coefficients and variances.In all cases, basic ideas and equations are presented along with sample problems that illustrate the major ideas and provide practice on expected exam questions. Time: Approximately 3 hours | Difficulty Level: Medium


13 videos, 1 reading expand


  1. Reading: Learning Objectives
  2. Video: Basic Parameters
  3. Video: Permutation and Combinations
  4. Video: Probability: Laws and Examples
  5. Video: Probability: Bayes Theorem
  6. Video: Probability Distributions: Density Functions
  7. Video: Probability Distributions: Expected Values
  8. Video: Probability Distributions:Binomial Distribution
  9. Video: Probability Distributions:Normal Distribution
  10. Video: Probability Distributions:Central Limit Theorem
  11. Video: Probability Distributions:Other Distributions
  12. Video: Confidence Levels
  13. Video: Hypothesis Testing
  14. Video: Linear Regression

Graded: Probability and Statistics Supplemental Questions

WEEK 4


Statics



This module reviews the principles of statics: Forces and moments on rigid bodies that are in equilibrium. We first discuss Newton’s laws and basic concepts of what is a force, vectors, and the dimensions and units involved. Then we consider systems of forces and how to compute their resultants. We discuss the main characteristics of vectors and how to manipulate them. Then the meaning and computation of moments and couples. We discuss the concept of equilibrium of a rigid body and the categories of equilibrium in two dimensions. We show how to draw a meaningful free body diagram with different types of supports. Then how to analyze pulleys and compute static friction forces and solve problems involving friction. The concept and major characteristics of trusses are discussed, especially simple trusses, and we show how to analyze them by the method of joints and the method of sections. Finally, we analyze the geometrical properties of lines, areas, and volumes that are important in statics and mechanics of materials. These are moments of inertia, centroids, and polar moments of inertia of simple and composite objects. In all cases, basic ideas and equations are presented along with sample problems that illustrate the major ideas and provide practice on expected exam questions.Time: Approximately 3 hours | Difficulty Level: Medium


9 videos, 1 reading expand


  1. Reading: Statics
  2. Video: Basic Concepts
  3. Video: Basic Concepts Continued
  4. Video: Moments and Couples
  5. Video: Equilibrium
  6. Video: Equilibrium Examples
  7. Video: Trusses
  8. Video: Trusses Method of Sections
  9. Video: Centroids and Moments of Inertia
  10. Video: Centroids and Moments of Inertia Continued

Graded: Statics Supplemental Questions

WEEK 5


Mechanics of Materials



This module reviews the principles of the mechanics of deformable bodies. We first review the basic concepts of equilibrium and stresses and strains in prismatic bars under axial loading. Then we discuss the major mechanical properties of common engineering materials, particularly the diagrams for normal stress and strain leading to Hooke’s Law, and their relation to lateral strain through Poisson’s ratio. Shear stresses and their relation to shear strains are then presented. We then analyze in detail deformations and stresses in axially loaded members. This includes uniform and nonuniform loading for statically determinate and indeterminate structures. Thermal effects are then considered: expansion and contraction under temperature changes and the stresses that may develop both with and without prestresses. Stresses on inclined planes under axial loadings and the resulting maximum and minimum normal and shear stresses that result are then discussed. Torsion, the twisting of circular rods and shafts by applied torques is then analyzed. We show how to calculate the angle of twist and shear stress as functions of rod properties and shape under uniform and nonuniform torsion. Applications to power transmission by rotating shafts are presented. We then discuss how shear forces and bending moments arise in beams subject to various loading types and how to calculate them. This is then generalized to local forms of the equilibrium equations leading to rules for drawing shear force and bending moment diagrams. Finally, we compute bending stresses in beams. Strains due to bending and their relation to curvature are first discussed. This is used to compute the bending stresses and their relation to the applied bending moment and beam material and cross sectional properties. This includes a review of computation of centroids and moments of inertia of various areal shapes. We complete this module with a discussion how shear stresses arise in beams subject to nonuniform bending and how to compute them. In all cases, basic ideas and equations are presented along with sample problems that illustrate the major ideas and provide practice on expected exam questions. Time: Approximately 4 hours | Difficulty Level: Medium


14 videos, 2 readings, 1 practice quiz expand


  1. Reading: Learning Objectives
  2. Video: Stresses and Strains: Introduction
  3. Video: Stresses and Strains: Mechanical Properties
  4. Video: Stresses and Strains: Shear Stress
  5. Video: Axial Loadings: Axial Loaded Members
  6. Video: Axial Loadings: Statically Indeterminate Structures
  7. Video: Axial Loadings: Thermal Effects and Stresses on Inclined Surfaces
  8. Video: Torsion: Circular Bars in Pure Torsion
  9. Video: Torsion: Nonuniform Torsion and Power
  10. Video: Shear Force and Bending Moments: Introduction to Bending of Beams
  11. Video: Shear Force and Bending Moments: Shear force and Bending Moment Diagrams
  12. Video: Stresses in Beams: Strains in Pure and Nonuniform Bending
  13. Video: Stresses in Beams: Strains in Pure and Nonuniform Bending (continued)
  14. Video: Stresses in Beams: Stresses, Moment-Curvature Equation, and Geometric Properties
  15. Video: Stresses in Beams: Digression (Centroids and Moments of Areas)
  16. Reading: Earn a Georgia Tech Badge/Certificate/CEUs
  17. Practice Quiz: Mechanics of Materials Supplemental Questions


WEEK 6


Fluid Mechanics



This module reviews the basic principles of fluid mechanics particularly the topics covered in the FE Exam. It first discusses what a fluid is and how it is distinguished from a solid, basic characteristics of liquids and gases, and concepts of normal and shear forces and stresses. The major fluid properties are then discussed. Next fluid statics are addressed: pressure variation in homogeneous and stratified fluids and application to manometers; forces on submerged plane surfaces and buoyancy forces on fully and partially submerged objects.Flowing fluids are then covered. This includes the equations for conservation of mass (the continuity equation) and energy (the Bernoulli equation). These are then applied to velocity and flow measuring devices: the Pitot tube, and Venturi and orifice meters.The final topic is similitude and dimensional analysis. This includes concepts of fundamental dimensions and dimensional homogeneity, the Buckingham Pi theorem of dimensional analysis, and the conditions for complete similitude between a full-scale prototype flow situation and a small scale model.In all cases, basic ideas and equations are presented along with sample problems that illustrate the major ideas and provide practice on expected exam questions.Time: Approximately 6 hours | Difficulty Level: Medium


19 videos, 1 reading expand


  1. Reading: Fluid Mechanics
  2. Video: Fluid Properties- Introduction
  3. Video: Fluid Properties-Density and Pressure
  4. Video: Fluid Properties-Stresses Viscosity
  5. Video: Fluid Properties-Surface tension
  6. Video: Fluid Properties-Units and other properties
  7. Video: Fluid Statics- Introduction and Pressure Variation
  8. Video: Fluid Statics-Application to manometers and barometers
  9. Video: Fluid Statics-Forces on submerged plane surfaces
  10. Video: Fluid Statics-Forces on submerged plane surfaces continued
  11. Video: Fluid Statics-Buoyancy and stability
  12. Video: Continuity and Energy Equations: Continuity and mass conservation
  13. Video: Continuity and Energy Equations: Energy equation
  14. Video: Continuity and Energy Equations: Energy equation examples
  15. Video: Flow Measurement-Pilot tubes
  16. Video: Flow Measurement-Venturi meter
  17. Video: Flow Measurement-Orifice meter
  18. Video: Flow Measurement-Dimensions and units, Pi theorem
  19. Video: Flow Measurement-Similitude
  20. Video: Flow Measurement-Similitude examples

Graded: Fluid Mechanics Supplemental Questions

WEEK 7


Hydraulics and Hydrologic Systems



This module applies basic principles of fluid mechanics to practical problems in hydraulics, hydrology, and groundwater flow. We first discuss the generalized and one-dimensional momentum theorem and apply it to various typical problems. Flow in pipes and non-circular conduits is discussed beginning with the Bernoulli equation accounting for energy losses and gains. Calculation of head loss due to friction and minor losses due to valves and other accoutrements are presented. Friction losses are calculated for laminar Poiseuille flow and turbulent flow using the Moody chart; examples include computation of pressure drop in laminar pipe flow and turbulent water flow. Methods to calculate flow in pipe networks consisting of multiple connecting pipes and other fittings is then discussed with examples for parallel pipes. Pipes and turbines are then discussed along with their basic equations and definitions. Characteristic curves, especially of centrifugal pumps, are presented and it is shown how to match a pump to a system head.Flow in open channels are discussed including classification of flow types and prediction of uniform flow by the Manning equation. The use of specific energy concepts to solve gradually varying flows, and the importance of the Froude number and sub and supercritical flows are presented. Predictions of hydraulic jumps and flow over weirs are given.Hydrological principles include predictions of surface runoff by the curve number method and peak runoff by the rational formula. Groundwater principles include Darcy’s law for flow through porous media and prediction of drawdown by wells in confined and unconfined aquifers by the Dupuit and Thiem equations.In all cases, basic ideas and equations are presented along with sample problems that illustrate the major ideas and provide practice on expected exam questions.Time: Approximately 3 hours | Difficulty Level: Medium


12 videos, 1 reading expand


  1. Reading: Hydraulics and Hydrological Systems
  2. Video: Momentum Theorem
  3. Video: Momentum Theorem Continued
  4. Video: Flowin Pipesand Conducts
  5. Video: Flow in Pipes
  6. Video: Flow in Pipes Continued
  7. Video: Pumps and Turbines
  8. Video: Pumps and Turbines Continued
  9. Video: Flow in Open Channels
  10. Video: Flow in Open Channels Continued
  11. Video: Hydrology
  12. Video: Groundwater
  13. Video: Groundwater Continued

Graded: Hydraulics Hydrology Supplemental Questions

WEEK 8


Structural Analysis



This module reviews basic principles of the structural analysis of trusses and beams. It builds on material covered in Statics (Module 6) and Mechanics of Materials (Module 8). We first review the conditions for static equilibrium, then apply them to simple trusses and beams. We then consider the deflections of beams under various types of loadings and supports. We derive the differential equations that govern the deflected shapes of beams and present their boundary conditions. We show how to solve the equations for a particular case and present other solutions. The method of superposition and its application to predicting beam deflection and slope under more complex loadings is then discussed. Finally the conditions for static determinacy and indeterminacy are presented along with example applications to trusses and beams. In all cases, basic ideas and equations are presented along with sample problems that illustrate the major ideas and provide practice on expected exam questions.Time: Approximately 2.5 hours | Difficulty Level: Medium


8 videos, 2 readings expand


  1. Reading: Structural Analysis
  2. Video: Static Review: Equilibirum
  3. Video: Static Review: Trusses
  4. Video: Static Review: Beams
  5. Video: Beam Deflections: Differential Equations
  6. Video: Beam Deflections: Solutions to Differential Equations
  7. Video: Beam Deflections: Examples
  8. Video: Beam Deflections: Methods of Superposition
  9. Video: Static Determinacy: Trusses and Beams
  10. Reading: Where to go from here

Graded: Structural Analysis Supplemental Questions

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