ATOC 5600 Physics and Chemistry of Clouds and Aerosols

Description

• cours magistral
• exposé - matière potentielle : material from the current literature
• leçon - matière potentielle : scavenging of aerosols
• exposé
• revision
• leçon - matière potentielle : deposition velocities

ATOC 5600 Physics and Chemistry of Clouds and Aerosols Brian Toon Duane D-245 492-1534 Meets Tuesday and Thursday 2-3:15 Duane G-318

• vapor pressure equations -deliquesence -crystallization of salts -surface tension -kelvin effect b.
• brownian coagulation
• radiative effects -ventilation effects -shape effects -mass transfer limitations
• aerosols - size distributions - integrals of size distributions
• nucleation from the vapor
• solutions of the growth equations
• aerosols
• clouds

Sujets

• Cours magistral
• Exposé
• Révision
• Physics

Informations

• Publié par: nazak
• Nombre de lectures: 30
• Langue: English

Extrait

About the class
Presentation
Matrix algebra
Lecture 1 - Introduction
Department of Computer Science
University of Houston
January 18, 2008
1 Lecture 1 - IntroductionAbout the class
Presentation
Matrix algebra
Informations
Instructor : Bilel Hadri
Email : [e-mail]
Office : PGH 210
Office hours : 2:00pm - 2:30pm, 4:00pm-4.30pm on Tuesday and
Thursday
Phone : [phone] Lectures available at
http://www2.cs.uh.edu/~hadri
Class Responsible : Dr Marc Garbey
Office : PGH 501
2 Lecture 1 - IntroductionAbout the class
Presentation
Matrix algebra
Syllabus
1 Solving Systems of Linear Equations : Direct methods
Matrix Linear Algebra
LU and Cholesky factorization
Pivoting
2 Norms of Analysis of errors
3 Solving Systems of Linear Equations : Iteratives methods
Neumann Series and Iterative refinement
Jacobi
Gauss-Seidel
SOR
Steepest Descent and Conjugate Gradient Methods
4 Matrix Eigenvalue Problem
Power Method
Inverse power method
Schur’s and Gershogorin’s theorems
SOR
3 Lecture 1 - IntroductionAbout the class
Presentation
Matrix algebra
5 Orthogonal Factorizations and Least-Squares problems
Singular-Value Decomposition
Pseudoinverse
QR-Algorithm
Textbook: Numerical Mathematics and Computing, by Ward Cheney
and David Kincaid, published by Brooks/Cole publishing Company.
ISBN 0-534-35184-0
4 Lecture 1 - IntroductionAbout the class
Presentation
Matrix algebra
Organization
Homework: 3-4 homeworks
Learn how to design and implement a variety of numerical
algorithms by using MATLAB or similar
Quizz: 5
questions about the lectures.
Practice lecture every 2 weeks : writing and computer exercises
1 midterm
1 final
Grades : Final 40%, Midterm 30%, Quizz 15%, Homeworks 15%
5 Lecture 1 - IntroductionAbout the class
Presentation
Matrix algebra
History
Numerical analysis predates the invention of modern computers.
Linear interpolation was in use more than 2000 years ago.
Important algorithms like Newton’s method, Lagrange
interpolation polynomial, Gaussian elimination, or Euler’s
method.
Double precision tables were created to facilitates the numerical
computations : log, sine, cosine, tangente.
Mechanical calculators that evolved in electronic computers in
1940s were build.
Computers were then found to be used for other tasks....but it
influence greatly numerical analysis too since more complex
operations were possible.
6 Lecture 1 - IntroductionAbout the class
Presentation
Matrix algebra
Numerical analysis and Computer Science
Numerical analysis still drives research in pure computer science
fields, but it also had many other applications
1 Pure computer Science
Computer Architecture : Blue Gene, Earth Simulator
Languages and Compilers : Fortran since 1970s, Fortress
Data Structures : matrix, vectors, arrays
Algorithms : matrix-matrix, matrix-vector multiplications, scalar
product. Design of efficient library: Blas, Lapack
Parallel Computing : network, libraries, architectures
2 Applications
Image processing
Medical Imaging : thermal imaging, EEG
Computer Graphics : face and body modeling
Data Mining
7 Lecture 1 - IntroductionAbout the class
Presentation
Matrix algebra
Matrix definitions
A matrix is an array of numbers, denoted A and its(i, j) th
element is denoted by the corresponding lower-case alphabet
with subscripts ij :aij
A m× n matrix A contains m rows and n columns and can be
expressed as  
a 1 a 2 ... a n1 1 1
 a 1 a 2 ... a n2 2 2 
A= . . ... . . . .. . .
a a ... am1 m2 mn
An n× 1 (1× n) matrix is an n− dimensional column (row) vector
denoted z, and its i th element is denoted by the corresponding
lower-case alphabet with subscript i :z .i
For a matrix A, its i th column is denoted as a .i
A matrix is square if its number of rows equals the number of
columns.
A matrix is said to be diagonal if its off-diagonal elements.
8 Lecture 1 - IntroductionAbout the class
Presentation
Matrix algebra
Matrix operations
Given two m× n matrices A and B, A= B if a = b for every i, j.ij ij
TThe transpose of an m× n matrix A, denoted as A , is the m× n
Tmatrix whose(i, j) th element is the(j, i) th element of A . The
transpose of a column vector is a row vector; the transpose of a
scalar is just the scalar itself.
TA matrix A is said to be symmetric if A= A , i.e., a j= a i for alli j
i, j.
Given a scalar λ λA is defined by(λA) = λaij ij
A+B is defined by(A+ B) = a + bij ij ij
Pn
AB is defined by(AB) = a bij ik kjk=1
9 Lecture 1 - IntroductionAbout the class
Presentation
Matrix algebra
Equivalent systems
Given two systems of n equations with n unknown
Ax= b Bx= d
if two systems have the same solutions they are call equivalent
Elementary operations:
1 Interchanging two equations of a systems
2 Multiplying an equation by a non zero number
3 Adding to an equation a multiple of some other equation
Equivalent systems theorem
Theorem
If one system of equations is obtained from another by a finite
sequence of elementary operations then the two systems are
equivalent.
10 Lecture 1 - Introduction