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Quantum Engineering Year 0: Mathematical Foundations Month 2Day 51

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Year 0·Month 2·Week 4

Day 51: Line Integrals

Day 51 of 2,016~8 min read

Learning Objectives

•Parametrize curves in 2D and 3D
•Compute scalar line integrals ∫_C f ds
•Compute vector line integrals ∫_C **F** · d**r**
•Calculate work done by a force field
•Understand path independence for conservative fields

Today's Schedule (7 hours)

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1 Parametrizing Curves 2 Arc Length Element 3 Scalar Line Integral Scalar Line Integral Examples Example 1 Line Segment Example 2 Circle Vector Line Integrals 4 Definition 5 Physical Interpretation Work 6 Orientation Matters Vector Line Integral Examples Example 3 Work Done Example 4 Component Form Fundamental Theorem for Line Integrals 7 The Theorem 8 Path Independence 9 Equivalent Conditions Fundamental Theorem Examples Example 5 Using the Fundamental Theorem Example 6 Checking Path Independence Practice Problems Level 1 Scalar Line Integrals Level 2 Vector Line Integrals Level 3 Fundamental Theorem Level 4 Applications Level 5 Theory Answers Quantum Mechanics Connection Berry Phase Aharonov-Bohm Effect Daily Checklist Preview Tomorrow

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