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Quantum Engineering Year 0: Mathematical Foundations Month 1Day 23

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Year 0·Month 1·Week 4

Day 23: The Definite Integral and Area

Day 23 of 2,016~7 min read

Learning Objectives

•Understand Riemann sums as approximations of area
•Define the definite integral as a limit of Riemann sums
•Evaluate simple definite integrals from the definition
•Interpret definite integrals as signed area
•Apply basic properties of definite integrals

Today's Schedule (7 hours)

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1 The Challenge 2 The Strategy Approximation by Rectangles Riemann Sums 3 Setup 4 Types of Riemann Sums 5 Visual Representation Worked Example Computing a Riemann Sum The Definite Integral 6 Definition 7 Notation 8 Geometric Interpretation Properties of Definite Integrals Property 1 Reversing Limits Property 2 Same Limits Property 3 Constant Multiple Property 4 SumDifference Property 5 Additivity Property 6 Comparison Property 7 Bounds More Worked Examples Example 2 Evaluating from Definition Example 3 Using Geometry Example 4 Signed Area Practice Problems Level 1 Riemann Sums Level 2 Using Geometry Level 3 Properties Level 4 From Definition Level 5 Interpretation Answers Quantum Mechanics Connection Daily Checklist Preview Tomorrow

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