Lectures - Week 9
The Singular Value Decomposition Theorem
We know that eigenvalues are only dened for a square matrix. However, in this section
we want to dene an analogue of eigenvalues for a rectangular matrix. This will lead us
to our nal decompositio

Summary Analysis of SecurityNow! podcasts Symmetric Block Ciphers and HMACs
SecurityNow: Symmetric Block Ciphers
Steve Gibson and Leo Laporte start the podcast with commentary on a previous episodes scenario
challenge: would you be able to double-encrypt

Lectures - Week 14
Vector Form of Taylors Series, Integration in Higher Dimensions,
and Greens Theorems
Vector form of Taylor Series
We have seen how to write Taylor series for a function of two independent variables, i.e.,
to expand f (x, y) in the neigh

Lectures - Week 7
Eigenvalues
The Algebraic Eigenvalue Problem
There are two major problems in linear algebra solving a linear system Ax = b and the
eigenvalue problem which is stated below.
Given an n n matrix A, nd a scalar and a nonzero vector x such t

Lectures - Week 4
Matrix norms, Conditioning, Vector Spaces, Linear Independence,
Spanning sets and Basis, Null space and Range of a Matrix
Matrix Norms
Now we turn to associating a number to each matrix. We could choose our norms analogous to the way we

Lectures - Week 11
General First Order ODEs & Numerical Methods for IVPs
In general, nonlinear problems are much more dicult to solve than linear ones. Unfortunately many phenomena exhibit nonlinear behavior. We want to look at the general form
of a rst o

Lectures - Week 5
Four Basic Spaces
1. The column space (or equivalently the range) of A, where A is m n matrix is all
linear combinations of the columns of A. We denote this by R(A).
By denition (because it contains all linear combinations and is thus c

Introductory Lecture
Many phenomena (physical, chemical, biological, etc.) are model by dierential equations.
Recall the denition of the derivative of f (x) and its physical and graphical interpretation.
Example Suppose we are told that the population p

Lectures - Week 10
Introduction to Ordinary Dierential Equations (ODES)
First Order Linear ODEs
When studying ODEs we are considering functions of one independent variable, e.g., f (x),
where x is the independent variable and f is the dependent variable.

Lectures - Week 12
Single step and Multistep Methods for First Order Initial Value Problems
Runge-Kutta Methods
To obtain a more accurate scheme than Forward Euler, we must do additional work such
as additional function evaluations. Single step methods ta

Lectures - Week 15
Line Integrals, Greens Theorems
and a Brief Look at Partial Dierential Equations
Line Integrals
Another type of integral that one encounters in higher dimensions is a line integral where
we want to integrate a quantity along a given cur

Lectures - Week 13
Two Point Boundary Value Problems and
Functions of Several Variables
We now want to briey look at a linear second order BVP which is sometimes called a
two-point BVP because we are specifying conditions at the two endpoints of our domai

Lecture 3 - Vectors and Matrices
Last time we saw that if we have n equations in n unknowns then there are n2
coecients (some may be zero) and n right hand side components. To eciently study
linear systems we need to write all linear systems in a generic

ISC 4933-?/5935-? - Mathematical Tools for Scientic Computing
Fall 2014
Instructor:
Website:
Oce Hours:
TA:
Professor Janet Peterson
email: jpeterson@fsu.edu
oce: 444 DSL
phone: 850-644-1979
http:/www.sc.fsu.edu/jpeterson
T 11-12, R 3:30-4:00, other times

Lecture 5 - Triangular Factorizations & Operation Counts
LU Factorization
We have seen that the process of GE essentially factors a matrix A into LU . Now we
want to see how this factorization allows us to solve linear systems and why in many cases
it is

Lectures - Week 6
Linear Least Squares, Orthonormal vectors and the QR Decomposition
Linear Least Squares Method
As an example of an application where these interconnections between the spaces is useful,
we consider the linear least squares problem. Suppo

Lectures - Week 8
Eigenvalues & Numerical Methods for Finding a Single Eigenvalue
and the Singular Value Decomposition Theorem
Review
First we will summarize some of the facts we saw last week for the algebraic eigenvalue
problem of nding a nonzero vector

Chapter 1, Question 11: Describe two important data communications standards-making bodies. How
do they differ?
Answer:
The International Organization for Standardization (ISO) makes technical recommendations about data
communication interfaces. The Ameri