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Quantum Engineering Year 0: Mathematical Foundations Month 1Day 24

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Year 0·Month 1·Week 4

Day 24: The Fundamental Theorem of Calculus

Day 24 of 2,016~7 min read

Learning Objectives

•State both parts of the Fundamental Theorem of Calculus
•Understand why FTC is so important
•Apply FTC Part 1 to differentiate integrals
•Apply FTC Part 2 to evaluate definite integrals
•Use FTC with chain rule (extended version)

Today's Schedule (7 hours)

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Schedule Overview Learning Objectives Required Reading Primary Text Stewarts Calculus 8th Edition Video Resources 3Blue1Brown MIT OpenCourseWare 1801SC Professor Leonard The Fundamental Theorem of Calculus Why Its Fundamental FTC Part 1 Differentiation of Integrals Statement In Leibniz Notation Interpretation Proof Sketch FTC Part 1 Examples Example 1 Direct Application Example 2 Lower Limit is Variable Example 3 FTC with Chain Rule Example 4 Both Limits are Functions FTC Part 2 Evaluation of Integrals Statement Notation Why It Works FTC Part 2 Examples Example 5 Polynomial Example 6 Trigonometric Example 7 Exponential Example 8 Involving ln Example 9 Sum of Functions Example 10 Absolute Value Split Integral Summary The Two Parts Practice Problems FTC Part 1 FTC Part 2 Mixed Problems Answers Quantum Mechanics Connection Daily Checklist Reflection Questions Preview Tomorrow

Day 23Day 24 of 2,016Day 25