Undergraduate Lecture Notes in De Rham-Hodge Theory

Abstract

These lecture notes in the De Rham-Hodge theory are designed for a 1-semester undergraduate course (in mathematics, physics, engineering, chemistry or biology). This landmark theory of the 20th Century mathematics gives a rigorous foundation to modern field and gauge theories in physics, engineering and physiology. The only necessary background for comprehensive reading of these notes is Green's theorem from multivariable calculus.

28 pages, 4 figures, aded a new quantum section, minor corrections

References in corpus (3)

• A Matrix Model for 2D Quantum Gravity defined by Causal Dynamical Triangulations
• On the degrees of freedom of lattice electrodynamics
• The Partition Function for Topological Field Theories

Cited by in corpus (4)

• A conformal gauge theory of solids: insights into a class of electromechanical and magnetomechanical phenomena
• Cauchy-Maxwell equations: A unified field theory for coupled electromagnetism and elasticity
• Quantization due to the time evolution, with applications to Quantum Yang-Mills theory, Quantum Gravity and Classical Statistical Field Theory
• Relating the wave-function collapse with Euler's formula, with applications to Classical Statistical Field Theory