CE 536 Introduction to Numerical Methods for Civil Engineers
3 Credit Hours
This is an entry level graduate course intended to give an introduction to widely used numerical methods through application to several civil and environmental engineering problems. The emphasis will be on the breadth of topics and applications; however, to the extent possible, the mathematical theory behind the numerical methods will also be presented. The course is expected to lay foundation for students beginning to engage in research projects that involve numerical methods. Student will use MATLAB as a tool in the course. Experience with MATLAB is not required. The course will be taught in an interactive setting in a computer equipped classroom.
Prerequisite
For graduate students in civil engineering, there are no formal prerequisites or co-requisites. Undergraduate students should have a GPA of 3.0 or better and Junior standing. Discuss with instructor for any clarification regarding these requirements.
Course Objectives
Upon completion of the course, the students will be able to:
- Use MATLAB as a programming language for engineering problem solving.
- Describe and apply basic numerical methods for civil engineering problem solving.
- Develop algorithms and programs for solving civil engineering problems involving: (i) multi-dimensional integration, (ii) multivariate differentiation, (iii) ordinary differential equations, (iv) partial differential equations, (v) optimization, and (vi) curve fitting or inverse problems.
Course Requirements
Typically 7 homework assignments, 1 mini-project report, and a take-home final exam. A weighted average grade will be calculated as follows:
- Assignments – 40%
- Online Quizzes – 10%
- Mini-Project – 15%
- Final exam – 35%
+/- Grading system will be used. MATLAB software is required (see below under computer requirements).
Course Organization
| Module | Topic | Lectures: 75 min |
|---|---|---|
| 1 | MATLAB Basics | |
| 1.1 | General MATLAB commands and features | Lectures 1 – 2 |
| 1.2 | Simple Civil Engineering Examples | Lecture 3 |
| Assignment 1 – Matlab Basics | ||
| 2 | Numerical Integration and Differentiation | |
| 2.1 | Numerical integration techniques and civil engineering applications | Lectures 4 – 6 |
| Assignment 2 – Numerical Integration methods with applications | ||
| 2.2 | Numerical differentiation with applications in groundwater flow | Lecture 7 |
| Assignment 3 – Advanced numerical integration and differentiation with applications | ||
| 3 | Ordinary differential equations | |
| 3.1 | Runge-Kutta methods with applications in structural and environmental engineering | Lectures 8 – 9 |
| 3.2 | Stiff systems with applications in environmental engineering | Lecture 10 |
| 3.3 | Boundary value problems in structural and environmental engineering | Lectures 11 – 12 |
| Assignment 4 – ODE methods and applications | ||
| 4 | Partial differential equations | |
| 4.1 | Introduction to finite difference methods with civil engineering examples | Lectures 13 – 15 |
| 4.2 | Linear and non-linear system solution (direct and iterative methods) | Lecture 16 |
| 4.3 | Applications in groundwater flow and transport | Lecture 17 |
| 4.4 | Matlab PDE toolbox | Lecture 18 |
| 4.5 | Introduction to finite element methods with application to groundwater flow | Lecture 19 |
| Assignment 5 – PDE solution of groundwater applications | ||
| 5 | Optimization | |
| 5.1 | Direct methods with applications in environmental and structural engineering | Lecture 20 |
| 5.2 | Gradient based methods with applications in water resources engineering | Lectures 21 – 23 |
| 5.3 | Heuristic methods with applications in structural and water resources engineering | Lectures 24 – 25 |
| 5.4 | Design applications in structural and environmental engineering | Lecture 26 |
| Assignment 6 – Optimization applications in civil engineering | ||
| 6 | Curve fitting and inverse problems | |
| 6.1 | Linear and non-linear regression | Lecture 27 |
| 6.2 | Direct methods | Lecture 28 |
| 6.3 | Indirect methods | Lecture 28 |
| 6.4 | Applications in Civil Engineering | Lecture 29 |
| Assignment 7 – Curve fitting and inverse problems |
Recommended Textbook
Hardcover book:
Chapra, S.C., and R.P. Canale. Numerical Methods for Engineers, 7th edition, McGraw Hill, 2015. (Optional)
Updated: 1/11/2021