Spectral, Convolution and Numerical Techniques in Circuit Theory

1 Introduction2 Steady State Solutions to Circuit Problems3 Differential Equation Solution to Circuit Problems4 Series Expansion solution for Circuit Problems5 Numerical Differential Equation Solution to Circuit Problems6 Fourier Series and Periodic Functions7 Complex Fourier Series8 Fourier Transform9 Properties of the Fourier Transforms10 Further Examples/Topics on Fourier Transform11 Fourier Transform of Periodic Signals12 Approximate and Numerical Techniques in Fourier Transform13 Bandwidth14 Laplace Transform15 Using Complex Integration to Figure Inverse Laplace Transform16 Properties of Laplace Transform17 Laplace Transform of Periodic Functions18 Finding Inverse Laplace Transform via Partial Fractions19 Convolution20 Signal Construction in Terms of Convolution Integrals21 The Delta Function22 Impulse Response23 Time Convolution with Impulse Response24 Time Convolution with the Unit Step Response25 Sampling and the Sampling Theorem26 Transfer Functions27 The Phase28 Stability and Relation to Poles Placements29 Impulse Response as Configured from Inverse Transform30 Unit Step Response as Configured from Inverse Transform31 Pulse response32 Causal Cosine and Sine Response33 Causal, Periodic Pulse Response34 Slanted Unit Step Response35 Voltage/Voltage Filters36 RLC Circuits with Feedback37 Matrix Solution to MultiBranch Networks38 MultiSource Networks and Superposition39 Systems with Initial Conditions40 Application to Transistor Modeling and Circuits41 Op-Amp Filters42 Multi-port Network: Z-, Y-Parameters43 Scattering (s−) Parameters44 Application of Spectral Techniques to Solving 2D Electrostatic Problems45 Application of Spectral Techniques in Solving Diffusion Problems46 Application of Spectral Techniques in Solving the Wave EquationAppendixReferencesIndex