This Course at MIT

This Course at MIT pages provide context for how the course materials published on OCW were used at MIT. They are part of the OCW Educator initiative, which seeks to enhance the value of OCW for educators.

Course Overview

This page focuses on the course 18.330 Introduction to Numerical Analysis as it was taught by Professor Laurent Demanet in Spring 2012.

This is a lecture-based course on basic techniques for the efficient numerical solution of problems in science and engineering. It is a centerpiece of MIT’s undergraduate offerings in applied mathematics.

Course Outcomes

Course Goals for Students

  • Familiarity with numerical discretization of objects learned in calculus, such as integrals, derivatives, and differential equations
  • An idea of the size of the errors involved in numerical discretization
  • Familiarity with Fourier analysis and its numerical implementation

Possibilities for Further Study/Careers

The skills and knowledge taught in this course are fundamentally important for many scientists and engineers who go on to do simulations or data analysis in industry, as well as research in computational mathematics or computational engineering.

 

Curriculum Information

Prerequisites

Requirements Satisfied

Offered

  • Every spring

The Classroom

  • A classroom with a large sliding chalkboard at the front and rows of tables and chairs for students.

    18.330 is taught in a classroom that seats 35.

 

Student Information

On average, about 30 students take this course each year.

Breakdown by Year

Mostly sophomores and juniors in equal proportion; a few seniors

Breakdown by Major

1/3 math majors; 1/3 engineering majors; 1/3 from other sciences

Typical Student Background

  • Good quantitative instincts
  • Familiarity with calculus and elementary linear algebra, but not necessarily mathematical proofs

Ideal Class Size

Having more than 40 students tends to hinder class participation and interaction, while having fewer than 10 students carries the risk of the group not being lively enough to engage in a good discussion.

 
 

How Student Time Was Spent

During an average week, students were expected to spend 12 hours on the course, roughly divided as follows:

Lecture

3 hours per week
  • Two class sessions per week; 1.5 hours per class
  • 26 class sessions total
  • Concepts were often introduced with examples and motivation.
  • In-class time was primarily spent on blackboard lectures. Some key mathematical proofs were presented, but the course did not cover the notes in their entirety.
  • About one-eighth of class time was spent on numerical examples presented with MATLAB™ via the LCD projector.
 

Out of Class

9 hours per week
  • Problem Sets
  • Review of course material, such as lecture notes
  • Exam preparation
 

Semester Breakdown

WEEK M T W Th F
1 No classes throughout MIT. Class. Optional office hours. Class. No session scheduled.
2 No session scheduled. Class. Optional office hours. Class. No session scheduled.
3 No classes throughout MIT. Class. Optional office hours. Class and assignment due date. No session scheduled.
4 No session scheduled. Class. Optional office hours. Class and assignment due date. No session scheduled.
5 No session scheduled. Exam, no class session. Optional office hours. Class. No session scheduled.
6 No session scheduled. Class. Optional office hours. Class. No session scheduled.
7 No session scheduled. Class and assignment due date. Optional office hours. Class. No session scheduled.
8 No classes throughout MIT. No classes throughout MIT. No classes throughout MIT. No classes throughout MIT. No classes throughout MIT.
9 No session scheduled. Class and assignment due date. Optional office hours. Class. No session scheduled.
10 No session scheduled. Class. Optional office hours. Class and assignment due date. No session scheduled.
11 No classes throughout MIT. Class. Optional office hours. Class. No session scheduled.
12 No session scheduled. Class. Optional office hours. Class and assignment due date. No session scheduled.
13 No session scheduled. Class. Optional office hours. Class and assignment due date. No session scheduled.
14 No session scheduled. Class. Optional office hours. Class. No session scheduled.
15 No session scheduled. Class. Optional office hours. Class. No classes throughout MIT.
16 No classes throughout MIT. No classes throughout MIT. No classes throughout MIT. Exam, no classes throughout MIT. No classes throughout MIT.
Displays the color and pattern used on the preceding table to indicate dates when classes are not held at MIT. No classes throughout MIT
Displays the color used on the preceding table to indicate dates when class sessions are held. Class session
Displays the icon used on the preceding table which indicates dates when exams are held. Exam
Displays the color used on the preceding table to indicate dates when no class session is scheduled. No class session scheduled
Displays the symbol used on the preceding table which indicates dates when optional office hours are held. Office hours (optional)
Displays the symbol used on the preceding table to indicate dates when assignments are due. Assignment due date
 

Instructor Insights

I constantly questioned my students to get them to go through the steps of figuring out what the answer should be before they heard it from me.

—Prof. Demanet

Below, Prof. Laurent Demanet describes various aspects of teaching 18.330 Introduction to Numerical Analysis.

Teaching Style

This class had a mathematical edge, in contrast to what can be found in most textbooks. I constantly questioned my students to get them to go through the steps of figuring out what the answer should be before they heard it from me. I frequently linked to background material the students should know, as needed, even if it meant occasionally slowing down the expected pace of the class.

Balancing Fundamental Content with More Exciting Material

It is important to find the right tradeoff between important, enabling, but "soft" concepts (e.g., interpolation, quadrature, root-finding), and more interesting, intellectually substantive, "hard" material (e.g., Fourier series, sampling, and aliasing). Some old-fashioned topics such as Newton divided differences and Newton-Cotes formulas were deliberately trimmed out of this course to make more room for Fourier analysis.

I found it useful to show targeted numerical experiments with a clear message (live demos are good), in order for the students to gain a clear intuitive understanding of what the various numerical methods are accomplishing.