Unified Field Theory for the Engineer and the Applied Scientist

The term field dynamics refers to the branch of physics that deals with objects and phenomena large enough to be measured and observed and is developed from four–dimensional geometry. Research that was once a major interest within theoretical physics has since passed to differential geometry, where it now has a strong mathematical foundation in hyper–dimensional field theories.
In this unique monograph the experienced author, Professor Silverberg, illustrates that modern field theory is an equally valuable tool for engineers and applied scientists when the unsolved problems become increasingly cross disciplinary.
From the contents:
∗ 4D Space
∗ Relativity
∗ Energy
∗ Change
∗ Governing Equations
∗ Waves
∗ Particles
∗ Electrodynamics
∗ Mechanics
∗ Essay: An Evolving Science
Features 40 end–of–chapter problems –– with solutions free to lecturers.


Spis treści:
Preface.
1 4DSpace.
1.1 Convention.
1.2 Cartesian Coordinates.
1.3 Time as a Fourth Dimension.
1.3.1 Images.
1.3.2 Complex Numbers.
1.3.3 The Temporal Coordinate x4.
1.4 The Hypercube.
1.5 The 4D Right–hand Rule.
1.5.1 The Right–hand Indices.
1.6 Exercises.
2 Relativity.
2.1 Transformations.
2.2 Pure Rotations.
2.3 The Lorentz Transformation.
2.4 Historical Note about the Confusion Surrounding theMeaning of Time.
2.5 Exercises.
3 Energy.
3.1 Energy Density Field A.
3.2 Directional Derivative of A.
3.3 Gradient Vector S.
3.4 Energy Density Field Vector A.
3.5 Exercises.
4 Change.

4.1 Component Gradient Vector Gi.
4.2 Curvature Vector k.
4.3 The Electrical andMechanical Parts of dA/ds.
4.4 3D Space.
4.5 Summary.
4.6 Exercises.
5 Governing E quations.
5.1 2D Field Lines.
5.1.1 Comment on Bifurcations.
5.1.2 The Differential Form.
5.2 3D Field Lines.
5.3 4D Field Lines.
5.4 The Field Lines of Gi.
5.5 Uniqueness.
5.6 Exercises.
6 Waves.
6.1 Wave Superposition.
6.2 Rectangular Waves.
6.3 Spherical Waves.
6.4 Initial Value Problem.
6.4.1 Stiffness.
6.4.2 Damping.
7 Particles.
7.1 The Stationary Field Particle.
7.2 The Moving Field Particle.
7.3 The Flux of a Field Particle.
7.4 A Particle Exciting Another Field.
7.5 ParticleMotion at Nonrelativistic Speeds.
7.6 Exercises.
8 Electrodynamics.
8.1 Maxwell’s Equations in Differential Form.
8.2 Maxwell’s Equations in Integral Form.
8.3 Polarization.
8.3.1 3D Polarization.
8.4 The Lorentz Force.
8.5 Exercises.
9 Mechanics.
9.1 Noncoincident Observation.
9.2 Particle Interaction.
9.3 Newton’s Second Law.
9.4 Note About the Effect of Charge.
9.5 Inverse Square Laws.
9.5.1 Purely Electrical Behavior.
9.5.2 PurelyMechanical Behavior.
9.6 RelativisticMass.
10 Essay: An Evolving Science.
10.1 The Past.
10.1.1 Early Period.
10.1.2 Force.
10.1.3 Energy.
10.2 The Present.
10.2.1 The Starting Point.
10.2.2 Four–dimensional Space.
10.2.3 Energy in 4D Space is a Continuum.
10.2.4 The Particle is Itself an Idealized Field.
10.2.5 Mechanics and Electrodynamics are Parts of How Energy Changes.
10.3 The Future.
10.3.1 Scientific Impact.
10.3.2 Human Impact.
10.4 Closing Message about Scales of Observation.
Appendix A: Integral Theorems.
A.1 Longitudinal Integral Theorems.
A.1.1 Circulation.
A.1.2 Curl.
A.1.3 Coil.
A.2 Transverse Integral Theorems.
A.2.1 Flux and Divergence.
A.2.2 Strength and Dilatation.
Appendix B: Curvilinear Coordinates.
B.1 Principles.
B.2 Integral Theorems.
B.2.1 Circulation and Curl.
B.2.2 Coil.
B.2.3 Flux and Divergence.
B.2.4 Strength and Dilatation.
B.3 Continuity Equations.
B.4 Circular Coordinates.
B.4.1 Polar Coordinates.
B.4.2 Cylindrical Coordinates.
B.4.3 Spherical Coordinates.
B.4.4 Hyperpolar Coordinates.
B.4.5 Hypercylindrical Coordinates.
B.4.6 Hyperspherical Coordinates.
B.5 Exercises.
Solutions to Exercises.
References.
Index.

Nota biograficzna:
Larry Silverberg received his PhD in engineering mechanics from Virginia Polytechnic Institute in 1983. In 1995 he was awarded a professorship in mechanical and aerospace engineering at North Carolina State University, a post he still holds today. He is the author of some 50 journal articles, a mechanics book, and teaches classes on field theory to students in engineering and the applied sciences. Professor Silverberg′s primary research interests lie in field theory and dynamical systems.Larry Silverberg received his PhD in engineering mechanics from the Virginia Polytechnic Institute in 1983 and in 1995 was awarded a professorship in mechanical and aerospace engineering at North Carolina State University, a post he still holds today. He is the author of some 50 articles and one book, and has developed two graduate courses, teaching classes on field dynamics to students in engineering and the applied sciences.
Professor Silverberg′s primary research interests currently lie in field dynamics and the control of dynamical systems.

Okładka tylna:
The term field dynamics refers to the branch of physics that deals with objects and phenomena large enough to be measured and observed and is developed from four–dimensional geometry. Research that was once a major interest within theoretical physics has since passed to differential geometry, where it now has a strong mathematical foundation in hyper–dimensional field theories.
In this unique monograph the experienced author, Professor Silverberg, illustrates that modern field theory is an equally valuable tool for engineers and applied scientists when the unsolved problems become increasingly cross disciplinary.
From the contents:
∗ 4D Space
∗ Relativity
∗ Energy
∗ Change
∗ Governing Equations
∗ Waves
∗ Particles
∗ Electrodynamics
∗ Mechanics
∗ Essay: An Evolving Science
Features 40 end–of–chapter problems –– with solutions free to lecturers.