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Quantum Engineering Year 0: Mathematical Foundations Month 2Day 39

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Year 0·Month 2·Week 2

Day 39: Tangent Planes and Linear Approximation

Day 39 of 2,016~9 min read

Learning Objectives

•Find equations of tangent planes to surfaces
•Use tangent planes for linear approximation
•Understand differentiability in multiple variables
•Compute the total differential
•Apply linear approximation to error estimation

Today's Schedule (7 hours)

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On this page

1 Motivation 2 Surfaces as Graphs 3 Equation of the Tangent Plane 4 Why This Formula Tangent Plane Examples Example 1 Paraboloid Example 2 Exponential Surface Example 3 Trigonometric Surface Linear Approximation 5 The Linearization 6 Linear Approximation Formula 7 When Is It Valid Linear Approximation Examples Example 4 Approximating x y Example 5 Compound Interest Approximation The Total Differential 8 Definition 9 Interpretation 10 For Three Variables Differential Examples Example 6 Computing the Differential Example 7 Estimating Change Error Estimation 11 Propagation of Error 12 Relative Error Example 8 Error in Cylinder Volume Differentiability 13 Definition 14 Sufficient Condition Practice Problems Level 1 Tangent Planes Level 2 Linear Approximation Level 3 Differentials Level 4 Error Estimation Level 5 Theory Answers Quantum Mechanics Connection First-Order Perturbation Theory Uncertainty Propagation Daily Checklist Preview Tomorrow

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