Lecture 15 (Oct 26)

Gaussian elimination with partial pivoting.

LU decomposition, i.e. A=LU.

(P^T)LU decomposition, i.e. PA=LU.

Lecture 14 (Oct 21)

Lecture cancelled due to the weather condition.

HW4 due Oct 25 (Tue) or 26 (Wed):
Chapter 1: #29,30,31,32,33,34(a-d),35

Midterm will cover everything up to, including, materials from Lecture 12. Will NOT cover Gaussian Elimination.

Lecture 13 (Oct 19)

Gaussian elimination with backward substitution.

Operations count.

Lecture 12 (Oct 14)

Composite rules. Gaussian Quadrature.

Midterm

Date: Oct 28 (Friday)
Time: 130pm-230pm
Venue: Room 2407

Closed book and closed note.
No calculator.
Test up to and including materials from the lecture on Oct 21 (Friday) Oct 14 (Friday).

Lecture 11 (Oct 12)

Numerical integration: Trapezoidal rule, Midpoint rule, Simpson's rule. Their derivation based on polynomial interpolation and Taylor's expansion.

Degree of accuracy.

Composite rules.

HW4

Chapter 1: #29-33,34(a-d),35

Due: Oct 25 (Tue) or 26 (Wed) in your tutorial.

Midterm will cover every up to, and including, this HW set.

Lecture 10 (Oct 7)

Numerical differentiation.

Approach 2: Taylor's expansion.

Higher order derivatives.

Lecture 9 (Oct 5)

Numerical differentiation:

Approach 1: Given data points -> interpolating polynomial -> differentiate it and evaluate it at a given location.

Forward difference, backward difference, central difference.

Error bound based on polynomial interpolation.