Heaviside Operator: Initial Conditions 
Heaviside Operator: Initial Conditions
by Caltech
Video Lecture 26 of 38
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Date Added: August 21, 2017

Lecture Description

Heaviside Operator: Initial Conditions


Course Index

  1. Circuits Fundamentals: Definitions, graph properties, current & voltage, power & energy
  2. Circuits Fundamental: Passivity and Activity, KCL and KVL, Ideal Sources
  3. Circuits Fundamentals: Resistance, Ohm's law, linearity, time-variance, diode circuits.
  4. Nodal Analysis: ground, Y-Matrix, node voltage & stimulus vectors, Linear algebra, determinant
  5. Nodal Analysis: Examples, dependent sources, existence of a solution
  6. Nodal Analysis Continued: Nodal analysis, dependent sources, with voltage sources, super nodes
  7. Mesh Analysis & Diode Circuits: Mesh analysis, 3D networks, super mesh, diode circuit design
  8. Circuit Theorems: Superposition, Thévenin, Norton, Source Transformation, Network Equivalence
  9. Circuit Theorems: Source Transportation, Substitution Theorem, Maximum Power Transfer, Y-Delta
  10. Active circuits: Op-Amp, Feedback, Asymptotic Equality, Inverting and non-inverting amplifiers
  11. Singularity Functions: Introduction, Unit Step, Pulse, and Dirac Delta (Impulse) Functions
  12. Linear Systems: Dirac Delta, Sifting Property, Impulse Response, LTI, Convolution
  13. Linear Systems: Convolution, Examples of System Response, Convolution Examples
  14. Time-Domain Response: Capacitors and Inductors, RC Response, General 1st-Order System
  15. Time Domain Response: RC Step and Impulse Response
  16. Heaviside Operator: Introduction, basic examples
  17. Heaviside Operator: Low-Pass Operator, High-Pass Operator, Solving Differential Equations
  18. Heaviside Operator: Circuit Examples
  19. Heaviside Operator: Nodal Analysis Examples, Order of System, Oscilloscope Probe
  20. Impulse Response of 2nd Order System: Complex Numbers, Real Poles, Underdamped and Over-damped
  21. Heaviside Operator: Partial Fraction Expansion (PFE), Example
  22. Heaviside Operator: PFE with Multiple Roots, Example
  23. Heaviside Operator: Operator Catalog, Solving differential equation directly, Examples.
  24. Heaviside Operator: Time Delay, Convolution, Example
  25. Heaviside Operator: Operator Catalog Review, Convolution Example
  26. Heaviside Operator: Initial Conditions
  27. System Function: Forced and Natural Response, Poles and Zeros, Time Domain View, Laplace Xform
  28. Stability: Definition, Criterion, Poles Location, South-Hurwitz Method
  29. Laplace Transform Summary: Definition, Properties
  30. Intro to Network Synthesis, Complex Impedance,
  31. Sinusoidal Drive, Phasor Notations, Cascaded Systems, Intro to Bode Plot
  32. Bode Plot: Properties, Poles and Zeros, Resonance (2nd Order Peaking)
  33. Fourier Series and Fourier Transform. Intro, Basic Derivation
  34. Fourier Transform: Spectrum, Time and Frequency Duality, Impulse, Sinc, Box
  35. Fourier Transform: Modulation
  36. Fourier Transform: Sampling
  37. Time and Transfer Constants: Brief Introduction
  38. Course Brief Final Summary

Course Description

Topics include: fundamentals of circuits and network theory, circuit elements, linear circuits, terminals and port presentation, time-domain response, nodal and mesh analysis, sinusoidal response, introductory frequency domain analysis, transfer functions, poles and zeros, time and transfer constants, network theorems, introduction to state-space.


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