E19: Numerical Methods for Engineering Applications

Spring 2016

Lecture: T/TH 2:40-3:55PM, Hicks 211
Lab: W 1:15PM-4:00PM, Hicks 212

Instructor: Matt Zucker


Course description

This course is geared towards students who want to know how to transform a set of equations on a page into a working computer program. No particular programming experience is assumed, and no math courses beyond calculus. Techniques learned will be applied in a series of projects focused on engineering applications.

Look over the course syllabus for more information.

The topics below are subject to change. As we move through the course, I will update the list to reflect the new schedule, readings, and assignments.



Useful links


Class schedule

Week Dates Topics Reading Labs & HW
1 Jan 19, Jan 21
  • Introduction
    • Modeling and computation
    • Floating point representation
    • Taylor series
    • Error analysis
2 Jan 26, Jan 28
  • Root finding
    • Bracketing methods
    • Open methods
3 Feb 2, Feb 4
  • Linear systems of equations
    • Gaussian elimination
    • LU decomposition
  • Kiusalaas Sec. 2.1-2.3
  • Ham Sec. 7.1-7.8
4 Feb 9, Feb 11
  • Linear systems, cont'd.
    • Special matrices
    • Iterative methods
    • Singular Value Decomposition
  • Kiusalaas Sec. 2.5-2.8
  • Ham Sec 7.9-7.11
5 Feb 16, Feb 18
  • Curve fitting and interpolation
    • Least squares fitting
    • Cubic spline interpolation
  • Exam 1: date and time TBA
  • Kiusalaas Ch. 3 (but just skim through 3.2)
  • Ham Ch. 8
6 Feb 23, Feb 25
  • Optimization
    • Introduction to optimization
    • Single variable
    • Multivariable derivative-free methods
7 Mar 1, Mar 3
  • Optimization, cont.d'
    • Multivariable derivative-based methods
    • Nonlinear least squares
    • Constrained optimization
Spring break
8 Mar 15, Mar 17
  • Numerical differentiation and integration
    • Finite differences
    • Quadrature
9 Mar 22, Mar 24
  • Ordinary Differential Equations
    • Initial value problems
    • Runge-Kutta methods
  • Kiusalaas Sec 7.1-7.4
10 Mar 29, Mar 31
  • ODEs, continued
    • Lagrangian Mechanics
    • Simulating equations of motion
  • Forthcoming: Lagrangian Mechanics
11 Apr 5, Apr 7
  • Boundary value problems
    • Shooting Method
  • Exam 2: date and time TBA
  • Kiusalaas Sec. 8.1-8.2
12 Apr 12, Apr 14
  • Boundary value problems, cont'd
    • Finite Difference Method
  • Kiusalaas Sec. 8.3
13 Apr 19, Apr 21
  • Applied PDE's: fluid simulation
14 Apr 26, Apr 28
  • TBA
Finals TBA