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Quantum Engineering Year 0: Mathematical Foundations Month 3Day 62

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Year 0·Month 3·Week 1

Day 62: Computational Lab — First-Order ODEs in Python

Day 62 of 2,016~9 min read

Learning Objectives

•Solve ODEs symbolically with SymPy
•Solve ODEs numerically with SciPy
•Visualize solutions and direction fields
•Compare analytical and numerical solutions
•Implement ODE models for physical applications

Today's Schedule (7 hours)

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Schedule Overview Learning Objectives Setup Lab 1 Symbolic Solutions with SymPy 11 Basic ODE Solving 12 Initial Value Problems 13 Classifying and Solving Different Types Lab 2 Numerical Solutions with SciPy 21 Using odeint 22 Using solve_ivp Modern API Lab 3 Direction Fields and Phase Portraits 31 Direction Field Slope Field 32 Multiple Initial Conditions Lab 4 Physical Applications 41 Newtons Law of Cooling 42 RC Circuit 43 Mixing Problem Lab 5 Comparing Methods Lab Completion Checklist Lab Report Assignment Tomorrow Rest and Review

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