18.330 | Spring 2012 | Undergraduate
Introduction to Numerical Analysis

Syllabus

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Prerequisites

Calculus (18.01), Calculus (18.02), and Differential Equations (18.03). Some exposure to linear algebra (matrices) at the level of Linear Algebra (18.06) helps, but is not required. The assignments will involve basic computer programming in the language of your choice (Matlab® recommended; this class encourages you to learn Matlab if you don’t already know it).

Summary

Numerical analysis is the story of how functions, derivatives, integrals, and differential equations are handled as strings of numbers in the computer. At the heart of numerical analysis is an understanding of the speed of convergence of Taylor, Fourier, and other series expansions. Most scientists and engineers are sooner or later faced with computing tasks that require some knowledge of numerical analysis.

Topics

  • Series expansions: from calculus to computation
  • Integrals as sums and derivatives as differences
  • Interpolation, splines, and a second look at numerical calculus
  • Numerical methods for ODE, initial-value problems
  • Root finding, Newton’s method, boundary-value problems
  • Fourier transform, Fourier series, Shannon sampling theory
  • Bandlimited interpolation, spectral methods
  • Least-squares approximation
  • Principal component analysis

The class will NOT cover Linear Partial Differential Equations (18.303), and will contain much less linear algebra than the course Linear Algebra (18.06SC).

Grading

ACTIVITIES PERCENTAGES
Homework 50%
In-class midterm exam 20%
In-class final exam 30%

The homework problem sets will consist of both theoretical problems and numerical experiments. No late copy will be allowed. The lowest score will be dropped. Collaboration is allowed, but the codes and copies you turn in must be original and written by you.

The midterm and final exams are open-book. No calculators, phones, or computers are allowed.

Course Info
Departments
As Taught In
Spring 2012
Learning Resource Types
notes Lecture Notes
assignment Problem Sets
co_present Instructor Insights