Florida Gulf Coast University
U.A. Whitaker College of Engineering
Spring 2025
Last updated: Jan 3, 2025
Recorded Lessons: Link
EGN 6430 Advanced Engineering Analysis
CRN: 15845
Credit hours: 3
Class: Online - Asynchronous
Exam: Wednesday Apr 30 from 6:00 pm to 8:00 pm - In-Person at Holmes Engineering 330.
Instructor
Ahmed S. Elshall, PhD
Assistant Professor
Department of Bioengineering, Civil Engineering, and Environmental Engineering
U.A. Whitaker College of Engineering Joint Appointment with The Water School
Office: Holmes Hall 423 (inside 416)
Research Website: https://aelshall.weebly.com
Office Hours : Tuesday and Thursday 2:00 pm - 4:00 pm, and by appointment
Course Catalog Description
Methods of analysis applied to engineering problems. Topics include a review of vector calculus, linear algebra, analytical solutions and numerical integration of differential equations, finite integrals, and computer simulation and modeling.
Course Learning Objectives
At the completion of the course, students will be able to:
- Perform differentiation and integration using analytical and numerical methods
- Apply optimization techniques in engineering problem solving
- Apply ordinary differential equations and partial differentiation in engineering problem solving
- Understand and apply basic concepts of computer simulation and modeling to analyze engineering systems
- Use linear algebra and operations involving matrices to solve simultaneous equations
Course Schedule
These topics and number of assignments are tentative and subject to change based on class progress.
| Week |
Date (From - To) |
Topic |
Due date |
| 1 |
6-Jan - 12-Jan |
Course introduction; Dimensional analysis: Review |
Homework 1 |
| 2 |
13-Jan - 19-Jan |
Dimensional analysis: Pi theorem and physical models |
Homework 2 |
| 3 |
20-Jan |
Martin Luther King Holiday Observed (no classes) |
|
| 3 |
20-Jan - 26-Jan |
Differential calculus: Review |
Homework 3 |
| 4 |
27-Jan - 2-Feb |
Differential calculus: Optimization |
Homework 4 |
| 5 |
3-Feb - 9-Feb |
Differential calculus: Multivariable systems |
Homework 5 |
| 6 |
10-Feb - 16-Feb |
Differential calculus: Vector calculus |
Homework 6 |
| 7 |
17-Feb - 23-Feb |
Integral calculus: Review |
Homework 7 |
| 8 |
24-Feb - 2-Mar |
Integral calculus: Integral function |
Homework 8 |
| 9 |
3-Mar - 9-Mar |
Spring break (no classes) |
|
| 10 |
10-Mar - 16-Mar |
Differential equations: Laws of conservation |
Homework 9 |
| 11 |
17-Mar - 23-Mar |
Differential equations: Engineering applications |
Homework 10 |
| 12 |
24-Mar - 30-Mar |
Computer simulation and modeling: Mathematical models |
Homework 11 |
| 13 |
31-Mar - 6-Apr |
Computer simulation and modeling: Numerical solutions |
Homework 12 |
| 14 |
7-Apr - 13-Apr |
Linear algebra: Solving systems of linear equations |
Homework 13 |
| 15 |
14-Apr - 20-Apr |
Elective1 - Monte Carlo Simulation: Cost Estimation |
|
| 15 |
14-Apr - 20-Apr |
Elective1 - Regression analysis : Linear regession |
|
| 16 |
21-Apr - 27-Apr |
Exam review |
Homework 14 |
| 17 |
30-Apr |
In-class comprehensive final exam |
Final exam |
1 You are required to complete one of the two elective topics.
Topics
This course is designed for students in construction management, environmental engineering, and water resources engineering, with consideration that some students may not have completed a calculus course. Modules 0 to 6 are required. Module 7 and 8 are elective, and you only need to complete one of them.
Module 0 Course Introduction
Learning objectives: Understand the course structure and problem-solving approaches in engineering (1 contact hours)
- 0.1 Introduction to advanced engineering analysis:
- Overview of course structure and goals (Homework 1)
Moudle 1 Dimensional Analysis – 2 Weeks
Learning objectives: Apply dimensional analysis and Pi theorem to simplify complex engineering problems (4 contact hours)
- 1.1 Review of dimensional analysis:
- Dimensions and units (Homework 1)
- Dimensional homogeneity (Homework 1)
- 1.2 Pi theorem:
- Physical models, similarity, and Pi theorem (Homework 2)
- Pi theorem for dimensional analysis (Homework 2)
- Pi theorem, scaling laws and physical models (Homework 2)
Module 2 Differential Calculus – 4 Weeks
Learning objectives: Use derivatives for optimization, system analysis, and function approximation (10 contact hours)
- 2.1 Fundamentals of derivatives:
- Fundamental theorem of calculus: Basic principles connecting differentiation and integration, and conservation laws (Homework 3)
- Derivative rules: Limit of a function and Newton’s quotient, power rule, product rule, quotient rule, chain rule (Homework 3)
- Derivative of special functions: Exponential, log, and trigonometric functions (Homework 3)
- 2.2 Derivative tests:
- Singular points ans critical points: Derivative-based optimization, singular points, critical points, and derivative tests (Homework 4)
- Optimization: Basic problems of derivative-based optimization (Homework 4)
- Engineering applications: Optimization methods for groundwater remediation and model calibration (Homework 4)
- 2.3 Multivariable derivatives:
- Parametric equations: Derivatives of multivariable systems and parametric equations (Homework 5)
- Partial derivatives: Total derivatives and partial derivatives (Homework 5)
- Implicit differentiation: Implicit differentiation for problem solving (Homework 5)
- 2.4 Vector calculus:
- Gradient: Basic concepts and applications (Homework 6)
- Divergence: Basic concepts and applications (Homework 6)
- Curl: Basic concepts and applications (Homework 6)
- 2.5 Taylor series:
- Series expansion for function approximation: Taylor series and Maclaurin series (Homework 6)
Module 3 Integral Calculus – 2 Weeks
Learning objectives: Apply integration techniques to solve engineering problems involving accumulated quantities and series solutions for complex integral problems (5 contact hours)
- 3.1 Fundamentals of integrals:
- Integral of a function: Indefinite and definite integrals (Homework 7)
- Integrals of special functions: Exponential, log, and trigonometric functions (Homework 7)
- Elementary integration operations: Separation of terms and integration by parts (Homework 7)
- Higher order integration: Double integration, and moments of a function (Homework 7)
- Engineering applications: Bayesian model evidence and model selection in hydrology (Homework 8)
- 3.2 Integral functions:
- Infinite series solutions: Exponential function, error function, gamma function and Euler constant with engineering applications (Homework 8)
Module 4 Differential Equations – 2 Weeks
Learning objectives: Solve ordinary and partial differential equations for engineering applications (5 contact hours)
- 4.1 Fundamentals of differential equations:
- Basic terms: Order, linearity, and homogeneity of ordinary and partial differential equations (Homework 9)
- Laws of conservation: Conservation of mass, energy and momentum (Homework 9)
- Analytical solutions: Separation of variables and integrating factor (Homework 9)
- 4.2 Applications of differential equations:
- Engineering applications: Groundwater flow equation with analytical solutions (Homework 10)
- Predator-prey model: A critical thinking exercise (Homework 10)
Module 5 Computer Simulation and Modeling – 2 Weeks
Learning objectives: Develop and solve mathematical models using analytical and numerical methods (5 contact hours)
- 5.1 Introduction to Physics-based Modeling:
- Basics of formulating mathematical models from physical phenomena (Homework 11)
- Analytical and numerical solutions of mathematical model (Homework 11)
- Practical applications: Transport modeling of PFAS emerging contaminants (Homework 11)
- 5.2 Fundamentals to Physics-based Modeling:
- Boundary conditions (Homework 12)
- Finite difference method with Excel exercise (Homework 12)
- Inverse modeling with Excel exercise (Homework 12)
Module 6 Linear Algebra – 1 Weeks
Learning Objectives: Solve systems of linear equations using matrix and vector operations to analyze engineering systems (2.5 contact hours)
- 6.1 Introduction to Linear Algebra:
- Review of matrix Operations: matrices, determinants, and operations (Homework 13)
- Solving systems of linear equations (Homework 13)
- Distributed and lumped models: Heat transport and mass balance of a system of reactors (Homework 13)
Module 7 Monte Carlo Simulation – 1 Week
Learning Objectives: Use Monte Carlo methods for uncertainty analysis (2.5 contact hours)
- 7.1 Monte Carlo simulation for probabilistic cost estimation:
- Introduction to Monte Carlo simulation and probabilistic estimation
- Critical thinking exercise: Probabilistic estimate of farm profit with uncertainty quantification and sensitivity analysis
- Excel tutorial: Probabilistic estimate of farm profit with uncertainty quantification and sensitivity analysis (optional)
Module 8 Linear Regression – 1 Week
Learning Objectives: Apply linear regression to analyze data and evaluate model performance (2.5 contact hours)
- 8.1 Linear regression
- Model complexity and model selection
- Least squared method
- Critical thinking exercise: Is the Earth warming?
For more information, refer to course map
Course Materials
Slides and videos are available on Canvas. Key references used in preparing course materials include:
- Fluid Mechanics Fundamentals and Applications, 3rd Ed. by Yunus Cengel and John Cimbala, McGraw Hill (Module 1)
- Civil Engineering Reference Manual for the PE Exam, 14th Ed. by Michael R. Lindeburg, PPI - Kaplan (Module 2 and 3)
- Applied Hydrogeology, 5th Ed.by C. W. Fetter, David Kreamer, Waveland Press (Module 4 and 5)
- Numerical Methods for Engineers, 8th Ed. by Steven Chapra and Raymond Canale, McGraw Hill (Module 4, 5, 6 and 8)
- Uncertainty Quantification: Theory, Implementation, and Applications by Ralph C. Smith, SAIM (Module 7)
Assessment and Grading
Grading scale
The instructor may elect to employ a curve that favors the students.
| Grade |
Range |
Grade |
Range |
Grade |
Range |
| A |
94% or above |
B- |
80% to 82.99% |
D+ |
67% to 69.99% |
| A- |
90% to 93.99% |
C+ |
77% to 79.99% |
D |
60% to 66.99% |
| B+ |
87% to 89.99% |
C |
73% to 76.99% |
F |
Below 60% |
| B |
83% to 86.99% |
C- |
70% to 72.99% |
|
|
Assessment plan (100%)
- Participation 10%
- Homework 60%
- Final Exam 30%
General notes
- Grades Due from Faculty by Tuesday, 06 May 2024
- If you are falling behind, consult the academic calendar for the last day to drop.
- Incomplete grades are granted in exceptional circumstances (e.g., medical emergency)
Participation
For participation assessment, students are expected to:
- Watch recorded videos and fill-out exit tickets and participation log
- Complete the survey at the end of each module meaningfully to provide instructor with constructive feedback and suggestions
These form the majority of your participation grade.
Homework
A weekly homework will be posted on Canvas. Each assignment is due by Sunday at 11:59 pm, unless otherwise posted on CANVAS. Few assignments are designed to include self-directed learning opportunities. This is to give you the opportunity to explore and experiment with engineering problems of your interest.
Late Homework Policy
- If you encounter challenges that may affect your ability to submit on time, please communicate with the instructor as early as possible to explore possible accommodations.
- Deadline maybe extended for execused absences
- Unexecused late submissions received after the deadline will incur a penalty of 20% per day of the total possible points
- Once the solutions and grades are posted, late unexecused submissions will not be accepted, and a score of zero will be assigned
Exam
- A final comprehensive exam will be in-person, conducted with pencil and paper in FE exam format.
- The exam will only cover mandatory modules (Modules 1 to 6) and elective moudles are not included.
- The exam is two hours and consists of about 20 multiple-choice and true or false questions.
- The exam is open-book but no internet access is allowed.
- Only FE-approved calculators are permitted. That is a regular calculator and not a smart calculator or smart phone that is connected to the internet. Laptops are allowed as long as there is no internet access. Any form of internet access is prohibited.
- Study guide: If you can solve the exercises, practice problems, and homework, you will be prepared for the exam.
- Exam review will be posted on Canvas after the week of the last mandatory module.
- Receiving or providing unauthorized assistance, including using the internet, will result in a grade of zero on this exam. The academic dishonesty policy will apply.
- A makeup exam may be provided for students with an execused absence
Execused Absence Policy
- Absence excuse requires written documentation from a certified medical professional, faculty member, administration, coach, or athletic director.
- Absence will be execused after the verification of the submitted document
- Any attempt to falsify documents will be taken very seriously in accordance with FGCU policies and procedures
Course and Program Assessment
Program Learning Outcomes for the Master of Science in Engineering (MSE) Program are as follows:
Content/Discipline Knowledge and Skills (DK) – MSE graduates will be able to:
- Apply higher level math, science and engineering skills to research and/or design engineering systems, components, or processes to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability.
- Understand the professional and ethical responsibilities associated with engineering practice and engineering research.
- Use the techniques, skills, and modern engineering tools necessary for engineering practice and engineering research.
Content/discipline knowledge and skills are assessed at the program level using appropriate coursework including examinations, assignments and presentations.
Communication Skills (CS) – MSE graduates will be able to:
- Organize and relate ideas coherently in written, oral, and graphic form.
- Develop and present consistent arguments to diverse audiences.
Communication skills are assessed at the University, College, and Program levels through oral and written presentations, project reports, and other assignments throughout the curriculum.
Critical Thinking Skills (CT) – MSE graduates will be able to:
- Identify problems and the relevant information needed to solve them.
- Analyze and synthesize information, and draw reasoned inferences.
- Formulate and evaluate appropriate problem-solving strategies.
Critical thinking skills are assessed at the University, College, and Program levels through oral and written presentations, project reports, exams, and other assignments throughout the curriculum.
Policy for Academic Integrity Violations
- Academic dishonesty in assignments, projects, or exams will result in a grade of zero for that submission, and will be strictly addressed in line with FGCU policies and procedures.
- Familiarize yourself with the FGCU Student Guidebook that outlines the consequences for academic integrity violations.
Financial Aid Statement
As of fall 2015, all faculty members are required to use Canvas to confirm a student’s attendance for each course by the end of the first week of classes. Failure to do so will result in a delay in the disbursement of your financial aid. The confirmation of attendance is required for all students, not only those receiving financial aid.
Generative AI Use
Generative AI including large language models (LLMs) such as ChatGPT, Gimini, Claude, and DeepL should not be used in assignments and exams unless indicated by the text “Generative AI Permitted”. Students must cite the used generative AI tool, and failing to do so will be considered academic dishonesty. Check FGCU Generative AI policy for more details.
Core Syllabus Policies
FGCU has a set of central policies related to student recording class sessions, academic integrity and grievances, student accessibility services, academic disruption, generative AI, and religious observances that apply to all courses at FGCU. Be sure to review these online
FGCU Writing Lab
We’re here to help students, faculty, and staff become more confident writers. To this end, we offer a variety of free services including one-on-one sessions with expert writing consultants, on-demand presentations on a range of writing-related topics and a broad selection of handouts developed specifically for the needs of the FGCU community. https://www.fgcu.edu/academics/caa/writinglab/
HiPerGator AI: Access the fastest artificial intelligence supercomputer in higher education. FGCU is partnered with the University of Florida to provide faculty and students with unparalleled computing power. The possibilities are endless when applied to instruction, research, and course development. Please contact the University Help Desk to learn more.
Syllabus Change Policy
Except for changes that substantially affect implementation of the evaluation (grading) statement, this syllabus is a guide for the course and is subject to change with advance notice.