Introduction to Numerical Methods

Introduction and Review

1/17 Course overview
Course survey due
1/19 Skim Chapter 1 of NCM
Introduction to MATLAB

1/24 Read Sections 1.1-1.3
Review of calculus and finite arithmetic
1/26 MATLAB exercises

Solutions of Equations in One Variable

1/31 Read Section 2.1
Watch Bisection example

Bisection method
2/2 Read Section 2.3
Newton's method
Problem Set 1 due

2/7 Read Sections 4.1-4.7 of NCM
MATLAB's fzero
Quiz 1
2/9 Read Section 2.4
Error analysis for iterative methods

Interpolation and Polynomial Approximation

2/14 Read Section 3.1
Interpolation and the Lagrange polynomial
2/16 Read Section 3.3
Divided differences
Problem Set 2 due

2/21 Read Section 3.4
Hermite interpolation
Quiz 2
2/23 Read Sections 3.1-3.5 of NCM
MATLAB interpolation

Numerical Differentiation

2/28 Read Section 4.1
Numerical differentiation
3/1 Read Section 4.2
Richardson's extrapolation
Problem Set 3 due

Midterm

3/6 MIDTERM
3/8 No class

3/13 SPRING BREAK
3/15 SPRING BREAK

Numerical Integration

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

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

Numerical Optimization

All readings in this module are from the Optimization Chapter posted in Canvas

4/3 Fundamentals of optimization
4/5 Read Sections B.1.1, B.1.2, and B.2
Multivariable calculus
Problem Set 4 due

4/10 Read Sections B.3.1, B.3.2, and B.3.3
Gradient descent and Newton's method
Quiz 4
4/12 No class

4/17 Read Sections B.3.4 and B.3.5
Quasi-Newton methods and L-BFGS
4/19 Read Section B.4
Comparison of algorithms
Problem Set 5 due

Project Presentations

4/24 Josh, Anna, Parry, Bjorn
4/26 Annie/Aadya, Mya, Raniery

Final Exam

5/1 Final review

5/7 FINAL EXAM (2pm)