Field Dynamics for the Engineer and the Applied Scientist

1. Space and Time
1.1 Convention
1.2 Cartesian Coordinates
1.3 The Meaning of Time
- Images
- Complex numbers
- The temporal coordinate
1.4 The 4D Cube
1.5 The 4D Right-Hand Rule
- The 2D, 3D, and 4D right-hand indices
1.6 Historical Note about the Confusion Surrounding the Meaning of Time

2. The Field
2.1 The Physical Quantity
2.2 The Material Field
2.3 Perception
2.4 The Material Field Vector
2.5 Continuity
- 2D field lines
- 3D field surfaces
- 4D field volumes
2.6 The Continuity Equation
2.7 The Material Field Vector
2.8 The Material Field Vector Equations

3. Singularities
3.1 Superposition
3.2 The Elementary Particle Field Vector
3.3 The Particle Field Vector as a Forcing Function

4. The Electrical-Mechanical Compliment
4.1 Directional Change of the Field Vector (Newton's Second Law)
4.2 Force at a Point Versus force on a Body (Newton's Third Law)
4.3 The Components of Change

5. Electrodynamics
5.1 3D Interpretation of 4D quantities
5.2 Excitation of the Field Vector (Maxwell's Equations)

6. Mechanics
6.1 Mass is Energy
6.2 Gravitation (Newton's Gravitational Law)

APPENDIX
7. Integral Theorems
7.1 Longitudinal Integral Theorems
- Circulation
- Curl
- Coil
7.2 Transverse Integral Theorems
- Flux and Divergence
- Strength and Dilatation

8. Curvilinear Coordinates
- Cartesian Curvilinear Coordinates
- The 4D Sphere

Larry Silverberg received his Ph.D. degree in engineering mechanics from the Virginia Polytechnic Institute in 1983. In 1995 he was appointed a professorship in mechanical and aerospace engineering at North Carolina State University (NCSU), where he still teaches. Professor Silverberg is the author of some 50 articles and one book, and has developed two graduate courses. His current primary research interests lie in field dynamics and the control of dynamical systems.