A0. A Practical Overview of Ordinary Differential Equations (ODEs)
Differential equations of one sort or another are in the background of most of the topics covered
in this course. Indeed, a big chunk of applied mathematics, and science in general, is co

Journal of Family Psychology
1999, Vol. 13, No. 1,3-19
Copyright 1999 by the American Psychological Association, Inc.
0893-32V99/$3.00
The Mathematics of Marital Conflict: Dynamic
Mathematical Nonlinear Modeling of Newlywed
Marital Interaction
John Gottma

1.1. Introducing Matlab. MATLAB is a numerical computing environment and
programming language. Created by The MathWorks, MATLAB allows easy matrix
manipulation, plotting of functions and data, implementation of algorithms, creation of
user interfaces, an

1.2. Examples. This section will provide some sample problems that use the elementary
ML commands and then assign some homework problems.
1. Collocation Method. This is a method of interpolating functions, or just data, using
basis functions and coefficie

Kortewegde Vries (KdV) equation:
Ut + Uxxx + 6 U Ux = 0 (water solitons)
Navier-Stokes:
v t v v p T f
NLSE:
iUz + (1/2) Uxx + N |U|2U = 0
(optical solitons)
A7. PDEs
This section covers some general principles and behavior patterns of first order PDEs i

A5. Delay Differential Equations and Difference Equations
This section provides an overview of systems with delay phenomena, and also introduces
difference equations. Delay and difference equations are related, as will be seen.
Starting with delay differ

Springfield Mixing Bowl
A6. Traffic Models
This section provides an account of traffic flow as described by conservation laws associated with
partial differential equations. This material is taken from the book Mathematical Models, by
Richard Haberman, S

4. Specialized Topics in ML. The ML portion of the course now concludes with some
miscellaneous special topics to further expand and enrich the ML experience. The topics
will be taken from both created and built-in ML files and commands.
(i) Roots (Zeros)

Part B: Estimation and Approximation
This part of the Notes will cover dimensional analysis and optimization. Not all topics
will necessarily be covered in a given semester, and some material will be left for
individual reading.
The notes are adapted from

Part A: Models
This part of the course will focus on physical models that are governed by differential and
difference equations. The differential equations models will include both ODEs and
PDEs.
A1. Systems of Ordinary Differential Equations (ODEs)
A sy

2. Plotting in ML. The section covers graphics and plotting. ML has very high level
graphics and a sophisticated graphical user interface (GUI). However, this intro will have
time only to go over the basics. Knowledge of even a few commands can be a big

Spontaneous traffic jam
A8. PDE Traffic Models
This section works out a simple model of traffic flow in detail. The physical situation is that of
cars stopped and queued at a traffic light when the light turns green. The discussion follows
Haberman, 73.

In mathematics and physics, a phase space,
introduced by J. Willard Gibbs (Gibbs
phenomenon, Gibbs free energy) in 1901, is a
space in which all possible states of a system are
represented, with each possible state of the
system corresponding to one uniqu

3. Matlab Scripts, Loops and Functions. This section covers several key ideas in ML
programming, all embedded in so-called M-files. An M-file is just a set of specific
commands stored in a file that can be edited, called and executed from the command line

PAGERANK BEYOND THE WEB
DAVID F. GLEICH
Abstract. Googles PageRank method was developed to evaluate the importance of web-pages
via their link structure. The mathematics of PageRank, however, are entirely general and apply to
any graph or network in any d

12/3/13
Burkhard Bilger: Inside Googles Driverless Car : The New Yorker
A REPORTER AT LARGE
AUTO CORRECT
Has the self-driving car at last arrived?
by Burkhard Bilger
NOVEMBER 25, 2013
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H
uman beings

Internat. J. Math. & Math. Sci.
Vol. 22, No. 3 (1999) 573578
S 0161-17129922573-2
Electronic Publishing House
ON THE OSCILLATION OF DELAY DIFFERENTIAL
EQUATIONS WITH REAL COEFFICIENTS
H. A. AGWO
(Received 30 August 1996 and in revised form 13 April 1998)

Part A: Models
This part of the course will focus on physical models that are governed by differential
and difference equations. The differential equations models will include both ODEs and
PDEs.
A1. Systems of Ordinary Differential Equations (ODEs)
A sy

Springfield Mixing Bowl
A6. Traffic Models
This section provides an account of traffic flow as described by conservation laws associated with
partial differential equations. This material is taken from the book Mathematical Models, by
Richard Haberman, S

Spontaneous traffic jam
A8. PDE Traffic Models
This section works out a simple model of traffic flow in detail. The physical situation is that of
cars stopped and queued at a traffic light when the light turns green. The discussion follows
Haberman, 73.

A5. Delay Differential Equations and Difference Equations
This section provides an overview of systems with delay phenomena, and also introduces
difference equations. Delay and difference equations are related, as will be seen.
Starting with delay differ

Kortewegde Vries (KdV) equation:
Ut + Uxxx + 6 U Ux = 0 (water solitons)
Navier-Stokes:
(v t + v v ) = p + T + f
NLSE:
iUz + (1/2) Uxx + N |U|2U = 0
(optical solitons)
A7. PDEs
This section covers some general principles and behavior patterns of first o

In mathematics and physics, a phase space,
introduced by J. Willard Gibbs (Gibbs
phenomenon, Gibbs free energy) in 1901, is a
space in which all possible states of a system are
represented, with each possible state of the
system corresponding to one uniqu

Exchange between Alice and the Cheshire
Cat:
"Would you tell me, please, which way I
ought to go from here?"
"That depends a good deal on where you
want to get to," said the Cat.
"I dont much care where-" said Alice.
"Then it doesnt matter which way you g

Part B: Estimation and Approximation
This part of the Notes will cover dimensional analysis and optimization. Not all topics
will necessarily be covered in a given semester, and some material will be left for
individual reading.
The notes are adapted from

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Symbols, Dimensions, and Units for Physical Quantities
Quantity
Acceleration
Angular Acceleration
Angular Displacement
Angular frequency and speed
Angular momentum
Angular velocity
Area
Displacement
Energy, total
Energy, kinetic
Energy, potential
Force
Fr

Global Energy Balance
What determines global surface
temperature?
Blackbody radiation
Energy emitted by an object depends on
temperature.
Energy Flux (W/m2)
= Energy/(Time x Area) = !T4
where ! = constant = 5.67x10-8 W/(m2K4)
1 W= 1 Joule/second (Energy/t