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* [[Optimization]]: Techniques used to design efficient circuits and systems. Applications include minimizing power consumption and maximizing signal integrity.
These methods are integral to systematically analyzing and improving the performance and functionality of electronic devices and systems.<ref>{{Cite
== Mathematical methods applied in foundational electrical laws and theorems ==
A number of fundamental electrical laws and theorems apply to all electrical networks. These include:<ref>{{Cite book |last=Kreyszig |first=Erwin |title=Advanced Engineering Mathematics |publisher=Wiley |year=2015 |isbn=978-0470458365}}</ref>
* [[Faraday's law of induction]]: Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil.
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* [[Norton's theorem|Norton's Theorem]]: Any two-terminal collection of voltage sources and resistors is electrically equivalent to an ideal current source in parallel with a single resistor.
* [[Thévenin's theorem|Thévenin's Theorem]]: Any two-terminal combination of voltage sources and resistors is electrically equivalent to a single voltage source in series with a single resistor.
* [[Millman's theorem|Millman's Theorem]]: The voltage on the ends of branches in parallel is equal to the sum of the currents flowing in every branch divided by the total equivalent conductance.
== Analytical methods ==
In addition to the foundational principles and theorems, several analytical methods are integral to the study of electronics:<ref>{{Cite book |last=James W. Nilsson, Susan Riedel |title=Electric Circuits |publisher=Pearson |year=2021 |isbn=9780137477845}}</ref><ref>{{Cite web |title=Mathematical Methods for Electrical Engineering {{!}} Lehrstuhl für Bildverarbeitung der RWTH Aachen |url=https://www.lfb.rwth-aachen.de/en/academics/lectures/mathematical-methods-for-electrical-engineering/ |access-date=2024-05-26 |language=en-US}}</ref>
* [[Network analysis (electrical circuits)]]: Essential for comprehending capacitor and inductor behavior under changing voltage inputs, particularly significant in fields such as signal processing, power electronics, and control systems. This entails solving intricate networks of resistors through techniques like [[Nodal analysis|node-voltage]] and [[Mesh analysis|mesh-current methods]].
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These methods build on the foundational laws and theorems provide insights and tools for the analysis and design of complex electronic systems.
== References ==
{{Reflist}}{{DEFAULTSORT:Mathematical Methods In Electronics}}
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