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Quantum Engineering Year 0: Mathematical Foundations Month 3Day 81

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Year 0·Month 3·Week 4

Day 81: Step Functions and Impulses

Day 81 of 2,016~6 min read

Learning Objectives

•Define and use the Heaviside step function
•Apply the second shifting theorem (t-shifting)
•Transform piecewise-defined functions
•Understand the Dirac delta function
•Solve ODEs with discontinuous or impulsive forcing

Today's Schedule (7 hours)

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Schedule Overview Learning Objectives Required Reading Primary Text Boyce DiPrima 11th Edition Part I The Heaviside Step Function 1 Definition 2 Laplace Transform of Step Function 3 Second Shifting Theorem t-Shifting Step Function Examples Example 1 Basic Step Example 2 Shifted Function Example 3 Piecewise Function Example 4 Rectangular Pulse Example 5 Writing Functions with Steps Part II The Dirac Delta Function 4 Definition Informal 5 Laplace Transform of Delta 6 Relation to Step Function Delta Function Examples Example 6 Impulse Response Example 7 Delayed Impulse Example 8 Switched Forcing Summary Shifting Theorems Practice Problems Level 1 Step Functions Level 2 Piecewise Functions Level 3 Delta Functions Level 4 Applications Answers Quantum Mechanics Connection Sudden Perturbation Fermis Golden Rule Daily Checklist Preview Tomorrow

Day 80Day 81 of 2,016Day 82