Mathematical methods in electronics
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Mathematical methods are integral to the study of electronics.
Mathematics in Electronics
Electrical Engineering careers usually include courses in Calculus (single and multivariable), Complex Analysis, Differential Equations (both ordinary and partial), Linear Algebra and Probability. Fourier Analysis and Z-Transforms are also subjects which are usually included in electrical engineering programs.
Basic applications
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Components
There are many electronic components currently used and they all have their own uses and particular rules and methods for use.
Complex numbers
If you apply a voltage across a capacitor, it 'charges up' by storing the electrical charge as an electrical field inside the device. This means that while the voltage across the capacitor remains initially small, a large current flows. Later, the current flow is smaller because the capacity is filled, and the voltage raises across the device.
A similar though opposite situation occurs in an inductor; the applied voltage remains high with low current as a magnetic field is generated, and later becomes small with high current when the magnetic field is at maximum.
The voltage and current of these two types of devices are therefore out of phase, they do not rise and fall together as simple resistor networks do. The mathematical model that matches this situation is that of complex numbers, using an imaginary component to describe the stored energy.
Signal analysis
- Fourier analysis. Deconstructing a periodic waveform into its constituent frequencies; see also: Fourier theorem, Fourier transform.
- Nyquist-Shannon sampling theorem.
- Information theory. Sets fundamental limits on how information can be transmitted or processed by any system.