San Francisco State University
Department of Physics and Astronomy
August 12, 2013
Vector Spaces in Physics
Notes
for
Ph 385: Introduction to
Theoretical Physics I
R. Bland
TABLE OF CONTENTS
Chapter I. Vectors
A. The displacement vector.
B. Vector additio
Vector Spaces in Physics
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Chapter 9. Fourier Series
A. The Fourier Sine Series
The general solution. In Chapter 8 we found solutions to the wave equation for a string fixed at
both ends, of length L, and with wave velocity v,
yn ( x, t ) = An si
Vector Spaces in Physics
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Chapter 8. Standing Waves on a String
The superposition principle for solutions of the wave equation guarantees that a sum of waves, each satisfying the wave equation, also represents a valid solution. In the next sectio
Vector Spaces in Physics
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Chapter 7. The Wave Equation
The vector spaces that we have described so far were finite dimensional. Describing position in
the space we live in requires an infinite number of position vectors, but they can all be repre
Vector Spaces in Physics
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Chapter 6a. Space-time four-vectors.
The preceding chapters have focused on a description of space in terms of three
independent, equivalent coordinates. Here we discuss the addition of time as a fourth
coordinate in "sp
Vector Spaces in Physics
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Chapter 6. Rotations and Tensors
There is a special kind of linear transformation which is used to transforms coordinates from one set of axes to another set of axes (with the same origin). Such a transformation is calle
Vector Spaces in Physics
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Chapter 5. The Inverse; Numerical Methods
In the Chapter 3 we discussed the solution of systems of simultaneous linear algebraic equations which could be written in the form Ax = C (5-1) using Cramer's rule. There is ano
Vector Spaces in Physics
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Chapter 4. Practical Examples.
In this chapter we will discuss solutions to two physics problems where we make use of techniques discussed in this book. In both cases there are multiple masses, coupled to each other so t
Vector Spaces in Physics
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Chapter 3. Linear Equations and Matrices
A wide variety of physical problems involve solving systems of simultaneous linear equations. These systems of linear equations can be economically described and efficiently solve
Vector Spaces in Physics
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Chapter 2. The Special Symbols ij and ijk , the Einstein
Summation Convention, and some Group Theory
Working with vector components and other numbered objects can be made easier
through the use of some special symbols an
Vector Spaces in Physics
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Chapter 1. Vectors
We are all familiar with the distinction between things which have a direction and those
which don't. The velocity of the wind (see figure 1.1) is a classical example of a vector
Figure 1-1. Where is t
Vector Spaces in Physics
8/12/2013
Chapter 10. Fourier Transforms and the Dirac Delta Function
A. The Fourier transform.
The Fourier-series expansions which we have discussed are valid for functions either defined over a
finite range ( T / 2 < t < T / 2 ,