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 their thesis projects that involve numerical methods. Student will use MATLAB or Python as a tool in the course.

Prerequisite

FGraduate standing in engineering. Discuss with instructor for any clarification regarding these requirements. Undergraduate students should have a GPA of 3.0 or better and Junior standing.

Course Objectives

Upon completion of the course, the students will be able to:

• Use MATLAB or Python 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 Organization and Scope

Module	Topic	Duration (75 Min)
1	Programming Basics	Weeks 1-2
1.1	General commands and features	Lectures 1-2
1.2	Simple Civil Engineering Examples	Lecture 3
	Assignment 1 – Programming basics
2	Numerical Integration and Differentiation	Weeks 2-3
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	Weeks 4-5
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	Linear and non-linear system solution	Week 6
4.1	Gaussian Elimination and Gauss-Jordan methods for linear system solution
4.2	Newton-Raphson method for nonlinear systems
	Assignment 5 – Linear and nonlinear systems
5	Partial differential equations	Weeks 7-8
5.1	Introduction to PDEs	Lecture 15
5.2	Finite difference methods and implementation of boundary conditions	Lecture 16
5.2	Solving one-dimensional convection-diffusion equation with finite difference and ODE approaches	Lecture 17-18
	Assignment 6 – PDE solution of groundwater applications
	Mini Project (4 Part Question Covering ODE/PDE)
6	Optimization	Weeks 8-9
6.1	Introduction	Lecture 19
6.2	Gradient based methods with applications in structural and water resources engineering	Lectures 21-23
6.3	Heuristic methods with applications in water resources engineering	Lectures 24-25
6.4	Applications in structural and environmental engineering	Lecture 26
	Assignment 7 – Optimization applications in civil engineering
7	Curve fitting and inverse problems	Week 10
7.1	Linear and non-linear regression	Lecture 27
7.2	Direct methods	Lecture 27
7.3	Indirect methods	Lecture 28
7.4	Applications in Civil Engineering	Lecture 28
	Final Exam (Take Home; Comprehensive)

Course Requirements

A weighted average grade will be calculated as follows:

• Assignments – 50%
• Project Assignment – 20%
• Final exam – 30%

+/- Grading system will be used. MATLAB software is required (see below under computer requirements).

Textbooks

Recommended Text(s):

Chapra, S.C and Clough, D. Applied numerical methods with Python for engineers and scientists, 1st edition, McGraw Hill, 2022.

or

Chapra, S.C. Applied numerical methods with MATLAB for engineers and scientists, 5th edition, McGraw Hill, 2023.

Optional Texts:

Chapra, S.C., and, R.P. Canale, Numerical methods for engineers, McGraw Hill, 8^th Edition, 2020. ($63 e-book)

Robert Johansson, Numerical Python: Scientific Computing and Data Science Applications with Numpy, SciPy and Matplotlib, 3^rd edition, 2024. ($30, paperback).

Palm W.J. III, Introduction to MATLAB for engineers, 3rd edition, McGraw Hill, 2010. ($14, paperback)

Updated: 10/17/2025