Why Mathematical Physics? - Part 1

In this episode we try to motivate mathematical abstraction in physics. We take the Maxwell Equations to be our jumping off point as we try to see if the equations can be packaged differently. We do so by observing their 'symmetries'. We are then aided in this journey of ours by our ol' reliable differential geometry.



0:00 Introduction
1:40 Electrodynamics
4:00 Symmetries and Maxwell Equations
5:15 Another Quantity
14:23 Abstraction - Role of Mathematical Physics
15:20 Lagrangians
21:40 Field Equations from the Lagrangian
26:40 Differential Forms
29:40 Electric and Magnetic Fields and Differential Forms
31:30 The Hodge Star Operator
34:34 Can E and B fields be interchanged in Differential Form Language
37:50 Electromagnetism in Even Dimensional Space

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