definition 28.25 Complex susceptibility
open in the book ·
parts/03-classical-mechanics/11-oscillations-waves.tex:756
· p. 953
- ground object -- no derivation owed
Rests on
- depends_on equation 28.24 eq:osc-lorentzian ¶
-
depends_on
proposition 17.52
Linear translation-invariant systems
¶
- depends_on definition 17.50 Convolution ¶
- depends_on definition 17.38 Schwartz space and tempered distributions ¶
-
depends_on
proposition 17.41
The identities physics uses
¶
-
depends_on
definition 17.40
Transform and derivative of a distribution
¶
- depends_on definition 17.38 Schwartz space and tempered distributions ¶ ↺
-
depends_on
proposition 17.39
The transform preserves $\mathcal{S}$
¶
- depends_on definition 17.38 Schwartz space and tempered distributions ¶ ↺
- depends_on proposition 17.30 Elementary properties ¶
- depends_on theorem 17.32 Fourier inversion ¶
- proves proof ch:15-fourier-integral-transforms@proof-25 ¶
-
depends_on
theorem 7.43
Fundamental theorem of calculus, II
¶
-
depends_on
definition 7.41
Antiderivative
¶
- depends_on corollary 7.36 cor:ana-mvt-consequences ¶
- depends_on definition 7.26 Derivative of a function at a point ¶
-
depends_on
theorem 7.42
Fundamental theorem of calculus, I
¶
- depends_on definition 7.26 Derivative of a function at a point ¶ ↺
- depends_on theorem 7.40 Continuous functions are integrable ¶
- depends_on theorem 7.24 Extreme value theorem ¶
- proves proof ch:05-real-analysis@proof-24 ¶
- proves proof ch:05-real-analysis@proof-25 ¶
-
depends_on
definition 7.41
Antiderivative
¶
- depends_on theorem 17.32 Fourier inversion ¶ ↺
- proves proof ch:15-fourier-integral-transforms@proof-26 ¶
-
depends_on
definition 17.40
Transform and derivative of a distribution
¶
- proves proof ch:15-fourier-integral-transforms@proof-33 ¶
Supports
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Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | eq:osc-lorentzian | declared | parts/03-classical-mechanics/11-oscillations-waves.tex:767 |
depends_on |
→ | Linear translation-invariant systems | declared | parts/03-classical-mechanics/11-oscillations-waves.tex:767 |