Elements for Physics

Written by: Albert Tarantola (Institut de Physique du Globe de Paris)

Fortunately for all of us, someone has preserved the work of Dr. Albert Taratola and continued to offer it freely to students around the world. Taratola taught at La Sorbonne with the Institut de Physcique du Globe de Paris, Princeton and the University of Santiago de Chile. Before his death in 2009, he had submitted the draft edition of the second edition for his textbook Elements for Physics. The textbook is complete, it simply was never “published” in the traditional sense of the word. Taratola was a strong proponent of the free exchange of knowledge and he thankfully posted this work-in-progress on his website. (The first edition also remains available on his website, though Taratola suggested students should utilize the second.)

From reading the Preface and looking over the table of contents this appears to be an advanced physics textbook. Taratola mentions discussing the material with other scholars and inventing terminology. From the preface, “Mathematical physics strongly relies on the notion of derivative (or, more generally, on the notion of tangent linear mapping). When taking into ac- count the geometry of the quality spaces, another notion appears, that of declinative. Theories involving nonflat manifolds (like the theories involv- ing Lie group manifolds) are to be expressed in terms of declinatives, not derivatives. This notion is explored in chapter 2.” As you can see, this is a rigorous treatment of the subject and is probably geared towards STEM majors.

Table of Contents for Elements for Physics Textbook

1. Geotensors
1.1 Linear Space
1.2 Autovector Space
1.3 Oriented Autoparallel Segments on a Manifold
1.4 Lie Group Manifolds
1.5 Geotensors
2. Tangent Autoparallel Mappings
2.1 Declinative (Autovector Spaces)
2.2 Declinative (Connection Manifolds)
2.3 Example: Mappings from Linear Spaces into Lie Groups
2.4 Example: Mappings Between Lie Groups
2.5 Covariant Declinative
3. Quantities and Measurable Qualities
3.1 One-dimensional Quality Spaces
3.2 Space-Time
3.3 Vectors and Tensors
4. Intrinsic Physical Theories
4.1 Intrinsic Laws in Physics
4.2 Example: Law of Heat Conduction
4.3 Example: Ideal Elasticity
A. Appendices
A.1 Adjoint and Transpose of a Linear Operator
A.2 Elementary Properties of Groups (in Additive Notation)
A.3 Troupe Series
A.4 Cayley-Hamilton Theorem
A.5 Function of a Matrix
A.6 Logarithmic Image of SL(2)
A.7 Logarithmic Image of SO(3)
A.8 Central Matrix Subsets as Autovector Spaces
A.9 Geometric Sum on a Manifold
A.10 Bianchi Identities
A.11 Total Riemann Versus Metric Curvature
A.12 Basic Geometry of GL(n)
A.13 Lie Groups as Groups of Transformations
A.14 SO(3) − 3D Euclidean Rotations
A.15 SO(3,1) − Lorentz Transformations
A.16 Coordinatesover SL(2)
A.17 Autoparallel Interpolation Between Two Points
A.18 Trajectory on a Lie Group Manifold
A.19 Geometry of the Concentration−Dilution Manifold
A.20 Dynamics of a Particle
A.21 Basic Notation for Deformation Theory
A.22 Isotropic Four-indices Tensor
A.23 9D Representation of 3D Fourth Rank Tensors
A.24 Some sketches of the configuration space (in2D)
A.25 Saint-Venant Conditions
A.26 Electromagnetism versus Elasticity

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Elements for Physics

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