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Quantum Engineering Year 0: Mathematical Foundations Month 2Day 41

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Year 0·Month 2·Week 2

Day 41: Computational Lab — Partial Derivatives and Visualization

Day 41 of 2,016~10 min read

Learning Objectives

•Visualize 3D surfaces and contour plots in Python
•Compute partial derivatives symbolically and numerically
•Visualize gradient vectors on contour plots
•Implement directional derivative calculations
•Visualize tangent planes

Today's Schedule (7 hours)

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Schedule Overview Learning Objectives Setup Lab 1 3D Surface Visualization 11 Basic Surface Plot 12 Saddle Surface 13 Multiple Surfaces for Comparison Lab 2 Symbolic Partial Derivatives 21 Using SymPy for Partial Derivatives 22 Evaluating at a Point 23 Chain Rule Verification Lab 3 Gradient Visualization 31 Gradient Field on Contour Plot 32 Gradient Shows Perpendicularity to Level Curves Lab 4 Directional Derivatives 41 Computing Directional Derivatives 42 Visualizing Directional Derivative Lab 5 Tangent Plane Visualization 51 Tangent Plane to a Surface Lab 6 Linear Approximation Accuracy Lab Completion Checklist Lab Report Assignment Tomorrow Rest and Review

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