Skip to main content
NC State Home
MAE 589 619 Computational Methods for MAE (now 514)
Fall 2026

MAE 589 619 Computational Methods for MAE (now 514)

3 Credit Hours

Hooman Tafreshi

Professor

919-515-6151

This course covers the basics of numerical methods used in solving ordinary differential equations (ODEs) and simple partial differential equations (PDEs). The course is tailored for the students in Mechanical and Aerospace Engineering discipline. The course is focused on practical applications of numerical methods as opposed to theory derivations and proofs. The course is comprised of multiple computational projects and homework sets, on topics such as mechanical vibrations, dynamical systems, heat and mass transfer, powders and particle flows, granular materials, fluid mechanics, and electrostatics.

Prerequisites

Undergraduate Differential Equations and familiarity with computer programing.

Course Learning Outcomes

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

  • Create finite difference equivalents of an ordinary differential equation (ODEs).
  • Create computer programs to solve ODEs using different Runge–Kutta methods.
  • Create systems of algebraic equations for systems of coupled ODEs and for simple partial differential equations (PDEs).
  • Create computer programs to solve the above systems of algebraic equations (i.e., linear algebra).
  • Solve engineering problems such as vibrating strings treated as systems of interconnected mass-spring-dampers (also referred to as discrete element modeling, DEM), unsteady heat conduction in 1-D and 2-D,
  • steady-state heat conduction in 2-D and 3-D, unsteady wave equation in 1-D, and 2-D.
  • Produce numerical data and visualize them in the form of plots, contours, and videos. The students will learn to interpret, critique, and communicate their data in different ways, e.g., least-square regression, interpolation, autocorrelation calculation (and classroom presentation).
  • Solve simple partial differential equations both numerically and analytically. The analytical methods include Fourier Series method, Laplace transform, and the similarity method.
  • Conduct 2-D or 3-D numerical projects using the discrete element method (DEM) and compare the simulation results with those of the above-mentioned analytical calculations.

Course Requirements

ComponentPercentageDetails
Homework20% 5 HW sets
(The additional HW set will be on analytical methods for PDEs)
Projects30%Two computational projects:
(The 1st project requires solving systems of coupled ODEs)
(The 2nd project requires solving PDEs)
Midterm25%One midterm (Closed book, equation sheets will be allowed)
Final 25%One comprehensive exam
(Closed book, equation sheets will be allowed)
(Graduate exam includes topics beyond those of the undergrad exam)
Extra credit Up to 10% For solving HW and project assignment in more ways than required

Textbooks

Required textbook: Numerical Methods for Engineers, Steven Chapra and Raymond Canale, 8th ed. (2021) Cost: ~$120. This textbook is required.
Optional book: Advanced Engineering Mathematics, Erwin Kreyszig, 10th edition (2011)

Created: 04/23/2026.