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Quantum Engineering Year 0: Mathematical Foundations Month 3Day 59

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Year 0·Month 3·Week 1

Day 59: Exact Equations and Special Methods

Day 59 of 2,016~8 min read

Learning Objectives

•Recognize exact differential equations
•Test for exactness using partial derivatives
•Solve exact equations by finding the potential function
•Apply integrating factors to make equations exact
•Solve Bernoulli equations via substitution

Today's Schedule (7 hours)

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On this page

1 Differential Form 2 Definition of Exactness 3 Test for Exactness 4 Solving Exact Equations Exact Equation Examples Example 1 Basic Exact Equation Example 2 With Initial Condition Example 3 Not Exact - Finding Integrating Factor Bernoulli Equations 5 Definition 6 Solution Method Bernoulli Examples Example 4 Bernoulli Equation Example 5 Another Bernoulli Homogeneous Equations 7 Definition 8 Solution Method Example 6 Homogeneous Equation Summary First-Order Methods Practice Problems Level 1 Exactness Test Level 2 Solve Exact Equations Level 3 Bernoulli Equations Level 4 Homogeneous Equations Level 5 Mixed Problems Answers Quantum Mechanics Connection Hamilton-Jacobi Equation Phase Space Daily Checklist Preview Tomorrow

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