Undergraduate Lecture Notes in De Rham-Hodge Theory
  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. 
Vladimir G. Ivancevic and Tijana T. Ivancevic