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COMPUTER C O NCEPTU A L TOOLS ENGINEERING

QuickTime™ and a TIFFare (Uncompressed)needed to see this decompressor picture. by Neil E. Cotter Research Assistant Professor Last Updated: 4/7/2018

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LAPLACE TRANSFORM DEFINITION STEP FUNCTIONS Piecewise function defs Example (pdf) TRANSFORM PAIRS: Table of basic transforms | (pdf) Impulse function Step function Sine Example (pdf) Example 2 (pdf) IDENTITIES: List | (pdf) Multiplication by constant Addition Differentiation Integration Delay Frequency shift Scaling time Multiplication by time (pdf) Example 1 (pdf) Example 2 (pdf) Example 3 (pdf) Example 4 (pdf) Example 5 (pdf) Example 6 (pdf) Example 7 (pdf) Example 8 | (pdf) Example 9 (pdf) INVERSE TRANSFORM †Definition Partial fractions COMPLEX ROOT IDENTITY (PDF) EXAMPLE 1 (PDF) EXAMPLE 2 (PDF) EXAMPLE 3 (PDF) EXAMPLE 4 (PDF) EXAMPLE 5 (PDF) EXAMPLE 6 (PDF) EXAMPLE 7 | (PDF) Matching forms EXAMPLE 1 (PDF) Complex roots EXAMPLE 1 (PDF) POLES AND ZEROS Impulse response vs pole location RC Filter Example 1 | (pdf) Example 2 (pdf) Example 3 | (pdf) Example 4 (pdf) INITIAL/FINAL VALUE THEOREMS †Initial value theorem (pdf) Example (pdf) Example 2 | (PDF) Example 3 (pdf) CIRCUITS s-domain circuit elements EXAMPLE (PDF) s-domain solutions EXAMPLE (PDF) EXAMPLE 2 (PDF) EXAMPLE 3 (PDF) EXAMPLE 4 (PDF) t-domain waveforms EXAMPLE (PDF) EXAMPLE 2 (PDF) EXAMPLE 3 (PDF) EXAMPLE 4 (PDF) EXAMPLE 5 (PDF) EXAMPLE 6 (PDF) Impulse function EXAMPLE (PDF) BASIS FUNCTIONS SINUSOIDS AS EIGENFUNCTIONS TRANSFER FUNCTIONS Magnitude and phase j encodes phase MATRIX DIFFERENTIAL EQUATIONS Transfer function stability Final value theorem State-space equations