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Quantum Engineering Year 0: Mathematical Foundations Month 2Day 38

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Year 0·Month 2·Week 2

Day 38: The Gradient and Directional Derivatives

Day 38 of 2,016~8 min read

Learning Objectives

•Define and compute the gradient vector
•Understand the geometric meaning of the gradient
•Compute directional derivatives
•Find the direction of maximum rate of change
•Apply gradients to optimization problems

Today's Schedule (7 hours)

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On this page

1 Definition 2 Notation 3 The Gradient as an Operator Gradient Examples Example 1 Polynomial Example 2 Exponential Example 3 Three Variables Directional Derivatives 4 Motivation 5 Definition 6 Formula Using the Gradient 7 Important Notes Directional Derivative Examples Example 4 Computing D_uf Example 5 Direction from Angle Properties of the Gradient 8 Maximum Rate of Change 9 Key Properties 10 Gradient Perpendicular to Level Curves More Examples Example 6 Maximum Rate of Change Example 7 Temperature Gradient Practice Problems Level 1 Computing Gradients Level 2 Directional Derivatives Level 3 Maximum Rate Level 4 Applications Level 5 Theory Answers Quantum Mechanics Connection The Momentum Operator Probability Current Potential Energy Daily Checklist Preview Tomorrow

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