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Maxwell's equations via differential forms.
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Classroom Contents
Differential Forms
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- 1 Differential Forms | Introduction and the Tangent Space
- 2 Differential Forms | What is a 1-form?
- 3 Differential Forms | The geometry of multiplying 1-forms.
- 4 Differential Forms | What is an m-form?
- 5 Differential Forms | What is an m-form?
- 6 Differential Forms | Algebraic Properties of the Wedge Product
- 7 Differential Forms | The dimension of the space of m-forms.
- 8 Differential Forms | What is a differential m-form?
- 9 Differential Forms | Integrating 2-forms
- 10 Differential Forms | Integrating m-forms.
- 11 Differential Forms | Examples of integrating 2-forms.
- 12 Differential Forms | Classic u-substitution via integrating 1-forms.
- 13 Differential Forms | Change of variables via integrating 2-forms.
- 14 Differential Forms | The exterior derivative.
- 15 Differential Forms | The product rule for the exterior derivative.
- 16 Differential Forms | Properties of the exterior derivative.
- 17 Differential Forms | The Hodge operator.
- 18 Differential Forms | The exterior derivative and vector calculus.
- 19 Differential Forms | The Hodge operator via an inner product.
- 20 Differential Forms | The Minkowski metric and the Hodge operator.
- 21 Maxwell's equations via differential forms.
- 22 Differential Forms | Integrals of m-forms over m-chains.
- 23 Differential Forms | Boundaries of m-cells and m-chains.
