Instructor

Dr. Kumar Mahinthakumar

Dr. Kumar Mahinthakumar

Civil, Construction, and Environmental Engineering

Phone: 919-515-7696
Fax: 919-515-7908
Email: gmkumar@ncsu.edu
Instructor Website
Research Website

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

ModuleTopicLectures: 75 min
1MATLAB Basics
 1.1General MATLAB commands and featuresLectures 1 - 2
 1.2Simple Civil Engineering ExamplesLecture 3
Assignment 1 - Matlab Basics
2Numerical Integration and Differentiation
 2.1Numerical integration techniques and civil engineering applicationsLectures 4 - 6
Assignment 2 - Numerical Integration methods with applications
 2.2Numerical differentiation with applications in groundwater flowLecture 7
Assignment 3 - Advanced numerical integration and differentiation with applications
3Ordinary differential equations
 3.1Runge-Kutta methods with applications in structural and environmental engineeringLectures 8 - 9
 3.2Stiff systems with applications in environmental engineeringLecture 10
 3.3Boundary value problems in structural and environmental engineeringLectures 11 - 12
Assignment 4 - ODE methods and applications
4Partial differential equations
 4.1Introduction to finite difference methods with civil engineering examplesLectures 13 - 15
 4.2Linear and non-linear system solution (direct and iterative methods)Lecture 16
 4.3Applications in groundwater flow and transportLecture 17
 4.4Matlab PDE toolboxLecture 18
 4.5Introduction to finite element methods with application to groundwater flowLecture 19
Assignment 5 - PDE solution of groundwater applications
5Optimization
 5.1Direct methods with applications in environmental and structural engineeringLecture 20
 5.2Gradient based methods with applications in water resources engineeringLectures 21 - 23
 5.3Heuristic methods with applications in structural and water resources engineeringLectures 24 - 25
 5.4Design applications in structural and environmental engineeringLecture 26
Assignment 6 - Optimization applications in civil engineering
6Curve fitting and inverse problems
 6.1Linear and non-linear regressionLecture 27
 6.2Direct methodsLecture 28
 6.3Indirect methodsLecture 28
 6.4Applications in Civil EngineeringLecture 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)

 

Computer and Software Requirements

Please review minimum computer specifications recommended by NC State University and Engineering Online.

 

Updated: 1/11/2021