Credits: 3


Restriction: Senior standing; and permission of ENGR-Mechanical Engineering department.
Creation of interactive graphic displays from the numerical simulation of mechanical engineering models. Brief description of each model provided, along with varied parameters to explore models' characteristics. Conclusions drawn from use of each interactive graphic. Mathematica language introduced and interwoven with the numerical simulation of the models, which will include: robotics and mechanisms, static response of beams, control systems, measurement systems, fluid flow, vibrations, geometric modeling, finite element analysis, and nonlinear phenomena.

Semesters Offered

Fall 2017, Fall 2019

Learning Objectives

To obtain a working knowledge of Mathematica to create interactive graphics that will provide an improved way to: (1) explore “what-if” scenarios; (2) examine a wide range of parameters and configuration combinations; (3) enhance one’s understanding of the model; (4) keep an audience’s attention during a presentation; and (5) exchange information within groups.

Topics Covered

  • Introduction to Mathematica:
    • Mathematica environment and basic syntax
    • list creation and manipulation
    • user-created functions, repetitive operations and conditionals
    • symbolic operations
    • numerical evaluation of equations
    • graphics
    • interactive graphics
    • geometry and FEA
  • Interactive graphics models
    • Animations
      • Modes shapes of two degrees-of-freedom systems
      • Unbalanced mass of a single degree-of-freedom system
      • Slider crank mechanism
    • Mathematics
      • Convolution
      • Streamlines, phase portraits, and nonlinear ordinary differential equations
      • Display of an oblate spheroidal coordinate system
      • Interpolation order and surface generation
    • Machine Design
      • Geared 5-bar mechanism
      • Cam profiles and synthesis
      • Deflection of linear springs in series
      • Milling simulation
    • Heat Transfer
      • Temperature distribution in fins with and without radiation
      • Steady-state temperature distribution in a slab with heated holes
    • Measurement Systems
      • Spectral content of periodic and aperiodic signals
      • Aliasing, filter selectivity, sampling rate, and signal spectrum
      • Frequency response errors in a transducer measuring system
    • Analysis of Structures
      • Static response of thin beams with an in-span spring
      • Symbolic static beam solutions as a function of boundary conditions
      • Beam properties of H-beams, channel beams, T-beams, Z-beams, and L-beams: moment of inertia, area, and center of gravity
      • Static loading of rectangular plates with two opposite edges hinged
    • Fluid Mechanics
      • oody diagram
      • Streamline patterns of uniform flow around a cylinder
      • Complex potentials and streamlines
      • Flow in open channels


Additional Course Information


Magrab, Dr. Edward B.


Edward B. Magrab, 2014, An Engineer’s Guide to Mathematica, John Wiley & Sons Ltd, UK.

Class/Laboratory Schedule 

  • Two 75 minute lectures per week
Last Updated By 
Edward Magrab, June 2017