THE MULTIPLE SPHERICAL PENDULUM
Thomas Wieting
Reed College, 2011
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The Double Spherical Pendulum
Small Oscillations
The Multiple Spherical Pendulum
Small Oscillations
Linear Mechanical Systems
1
The Double Spherical Pendulum
1 We imagine two sphe
DIFFERENTIAL FORMS ON R4
Thomas Wieting, 2011
Dierential Forms
01 One locates Events (t, x, y, z ) in Time/Space by specifying a coordinate
t for time and Cartesian coordinates x, y , and z for position. One measures t,
x, y , and z in meters. In one mete
The Diusion Equation
Thomas Wieting
Reed College, 2011
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Swarms
Simple Diusion
Prospects
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Swarms
Fundamentals
1 We imagine a Swarm of N particles in R3 , in random motion. We
describe the distribution of the particles in the Swarm by the number densi
FOURIER TRANSFORMS AND MAXWELLS EQUATIONS
Thomas Wieting
Reed College, 2011
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Introduction
Notation
Maxwells Equations Transformed
The Procedure
The Energy Equation
The Source Free Case
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Introduction
01 We will describe a procedure for solving
MATHEMATICS 322
Invitation to
ORDINARY DIFFERENTIAL EQUATIONS
Thomas Wieting
Reed College
2011
ORDINARY DIFFERENTIAL EQUATIONS
Chapter 0
OBJECTIVES AND PREREQUISITES
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Chapter 1
FUNDAMENTAL THEORY
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Chapter 2
SECOND ORDER LINEAR THEORY
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Chapter 3
STURM/
MATHEMATICS 322
THE KETTLE DRUM
Thomas Wieting, 2011
Bessel Functions of Integral Order
1
We begin by introducing the function:
(1)
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1
G(x, z ) = exp( x(z )
2
z
(x R, z C, z = 0)
We may present G as a Laurent Series in z , the coecients of which are
func
THE WAVE EQUATION IN THREE DIMENSIONS
Thomas Wieting, 2011
The Homogeneous Wave Equation
01 Let f and g be complex valued functions dened on R3 . We propose to
solve the Homogeneous Wave Equation:
tt (t, x, y, z ) ( )(t, x, y, z ) = 0
()
subject to the I