Instructor: Ronald Fulp

email: fulp@math.ncsu.edu

Phone Number: 515-2370

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

Office: HA219

Office Hours: 3:30—4:20 Tuesday, Thursday;

3:30-4:30 Monday, Wednesday. Other times by appointment

Prerequisites: MA 341 or 301; and MA 405.

Tentative Plan of Lectures:

5 days –Chapter 1, Euclidean geometry, Newton's Laws, forces

2 days – Chapter 2, review of differential and integral vector calculus

5 days – Chapter 3, Maxwell's equations, basic electromagnetism, potentials

5 days – Chapter 4, Mathematics of Special Relativity

5 days – Chapter 5, exterior algebra, differential forms, exterior derivatives pullbacks of forms, integrals of forms

5 days – Chapter 6, Hodge duality, potentials of E&M as forms,

Maxwell's equations via forms

? days - Generalized Stoke's Theorem, DeRham’s Theorem

Grading:

40% Homework

20% Test One Mid-term

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

20% Final Exam

SEE THE BACK OF THE PAGE

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 Tuesday, December 11, 8-11, in room HA263.