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Quantum Engineering Year 0: Mathematical Foundations Month 1Day 13

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Year 0·Month 1·Week 2

Day 13: Computational Lab — Derivatives in Python

Day 13 of 2,016~9 min read

Learning Objectives

•Compute derivatives symbolically using SymPy
•Implement numerical differentiation
•Visualize functions and their derivatives
•Understand the relationship between numerical and analytical derivatives
•Apply derivatives to optimization problems

Today's Schedule (7 hours)

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Schedule Overview Learning Objectives Setup Lab 1 Symbolic Differentiation with SymPy 11 Basic Symbolic Derivatives 12 Chain Rule Verification 13 Implicit Differentiation 14 Higher Derivatives and Taylor Series Lab 2 Numerical Differentiation 21 Forward Difference 22 Central Difference More Accurate 23 Second Derivative Lab 3 Visualization 31 Function and Derivative Plots 32 Tangent Line Visualization 33 Numerical vs Analytical Derivative Lab 4 Optimization Application 41 Finding Critical Points 42 Optimization Visualization Lab Completion Checklist Lab Report Assignment Tomorrow Rest and Review

Day 12Day 13 of 2,016Day 14