Introduction to Numerical Methods

Introduction and Review

1/18 Course overview
Course survey due

1/23 Read Sections 1.1-1.3
Review of calculus and finite arithmetic
1/25 Skim Chapter 1 of NCM
Introduction to MATLAB

Solutions of Equations in One Variable

1/30 Read Section 2.1
Bisection method
2/1 Read Section 2.3
Newton's method
Quiz 1

2/6 Read Sections 4.1-4.7 of NCM
MATLAB's fzero
2/8 Read Section 2.4
Error analysis for iterative methods

Interpolation and Polynomial Approximation

2/13 Read Section 3.1
Interpolation and the Lagrange polynomial
Problem Set 1 due
2/15 Read Section 3.3
Divided differences

2/20 Read Section 3.5
Cubic spline interpolation
Quiz 2
2/22 Read Sections 3.1-3.5 of NCM
MATLAB interpolation

Midterm

2/27 Midterm review
Problem Set 2 due
3/1 MIDTERM

3/6 SPRING BREAK
3/8 SPRING BREAK

Numerical Differentiation and Integration

3/13 Read Section 4.1
Numerical differentiation
3/15 Read Section 4.2
Richardson's extrapolation

3/20 Read Section 4.3
Elements of numerical integration
Quiz 3
3/22 Read Section 4.4
Composite numerical integration

3/27 Read Section 4.5-4.6
Romberg integration and adaptive quadrature methods
Project Proposal due
3/29 Read Sections 6.1-6.3 of NCM
MATLAB integration
Problem Set 3 due

Initial-Value Problems for Ordinary Differential Equations

4/3 Read Section 5.1
The elementary theory of initial-value problems
4/5 Read Section 5.2
Euler's method

4/10 Read Section 5.4
Runge-Kutta methods
Quiz 4
4/12 Read Section 5.5
Error control and the Runge-Kutta-Fehlberg method

4/17 Read Section 5.9 and Sections 7.1-7.2 of NCM
Higher-order and systems of differential equations
4/19 Read Sections 7.4-7.6 of NCM
MATLAB's ODE solvers
Problem Set 4 due

Project Presentations

4/24 Alex/Briana, Shiny, Ben/Steven, Andrea, Kedi
4/26 Jack, Liz/Dylan, Lauren, Koby, David, Bill

Final Exam

5/1 Final review

5/9 FINAL EXAM (9am)