Instructor:
Ronald Fulp

email: fulp@math.ncsu.edu

Phone Number: 515-3177 (No answer machine)

E-mail address: fulp@math.ncsu.edu

Office: SAS 4232

Office Hours: 4:00-5:00 Tuesday & Thursday, other times by appointment

Prerequisites: MA 242, MA 405, college physics

Tentative Plan of Lectures:

8 days –Euclidean geometry, Newton's Laws, forces

6 days – Basic electromagnetism, potentials, Gauss’ Theorem, Faraday, Amprere, and Maxwell’s equations in both integral form and vector form, reformulation of Maxwell’s equations in terms of differential forms on Newtonian spacetime

8 days –Basic mathematics of Special Relativity, geometric structure and Lorentz transformations

6 days – Formal approach to exterior algebra

and differential forms, exterior derivatives pullbacks of forms, integrals of forms. Maxwell’s equations using differential forms.

Grading:

40% Homework

20% Test One Mid-term

20% Test Two Composed of take-home problems given throughout the semester

20% Final Exam

Course Objectives: It is the purpose of this course to provide a critical mathematical analysis of the role of inertial frames in physics. It is our intent to understand how the inertial frames of Newton failed to provide a correct basis of electromagnetism and how this subsequently led to the development of special relativity. We will develop those concepts from special relativity and electromagnetism needed to meet this objective. A second objective of the course is to develop basic properties of Cartan’s exterior calculus and to show how this calculus and other concepts from modern mathematics can impact more traditional approaches to physics.

Homework will be done in groups and is due on Friday of each

week unless designated otherwise.

Final Exam is scheduled for

Thursday, December 8, 8-11, SAS 2225.