Add modeling sections with real-world differential equation applications to all chapters

[Copilot]

Adds practical modeling sections to each of the 15 chapters, demonstrating how differential equations arise from real-world phenomena and how to estimate parameters from data.

Structure

Each modeling section ({chapter-short-name}-model.ptx) contains:

• Real-world problem setup with explicit assumptions
• Derivation of the differential equation from first principles
• Parameter descriptions and physical interpretations
• Data collection/simulation activity for parameter estimation
• Analytical questions probing model behavior
• Final report requirements

Coverage

Modeling applications span multiple domains:

• Physical systems: Newton's cooling, projectile motion, spring-mass-damper, pendulum, RC circuits
• Population dynamics: Logistic growth, predator-prey, harvested populations, SIR epidemics
• Engineering: Crash absorption, thermostat control, resonance in structures, suspension design
• Medical: Pharmacokinetics and drug dosing schedules

Integration

Sections inserted before exercises in main.ptx:

<xi:include href="c3-di/sec-antiderivatives.ptx" />
<xi:include href="c3-di/sec-di-method.ptx" />
<xi:include href="c3-di/di-model.ptx" />
<xi:include href="c3-di/exercises-di.ptx" />

Each section is self-contained and can be used as in-class activities, homework assignments, or project work depending on course needs.

Warning

Firewall rules blocked me from connecting to one or more addresses (expand for details)

I tried to connect to the following addresses, but was blocked by firewall rules:

• webwork-ptx.aimath.org
  • Triggering command: /usr/bin/python python -m pretext build -t dev --clean (dns block)
  • Triggering command: /usr/bin/python python -m pretext build -t dev (dns block)

If you need me to access, download, or install something from one of these locations, you can either:

• Configure Actions setup steps to set up my environment, which run before the firewall is enabled
• Add the appropriate URLs or hosts to the custom allowlist in this repository's Copilot coding agent settings (admins only)

Original prompt

Create a PR that drafts a modeling section for each chapter. Name the file source/c{ChapterIndex}-{ChapterShortName}/{ChapterShortName}-model.ptx.

Each modeling section should be based on a real-world problem that can be modeled with an a differential equation from the same chapter. The section should include
(1) an introduction,
(2) a description of the problem,
(3) assumptions,
(4) the logical reasoning that leads to the construction of the DE that models the problem. Include a description of the parameters,
(5) design an in-class or out of class activity that simulates a modeling pipeline where students can collect data or are given data in order to estimate the model parameter(s).
(6) the activity should be paired with interesting analytical questions and culminate with a final report.
(7) include anything else that would be relevant.

This is intended to be a first draft that will be improved and refined.

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[Copilot]

Pull request overview

This PR adds practical modeling sections to each of the 15 chapters (c0-c14) of the differential equations textbook, demonstrating how differential equations arise from real-world phenomena. Each modeling section includes problem setup, derivation from first principles, parameter descriptions, data collection/simulation activities, analytical questions, and report requirements.

Changes:

• Added 15 new modeling files ({chapter-short-name}-model.ptx) covering diverse applications including Newton's cooling, projectile motion, population dynamics, pharmacokinetics, mechanical systems, and epidemic modeling
• Integrated 14 of these files into main.ptx before their respective exercise sections (c0-c13)
• Each file follows consistent structure with licensing header, PreTeXt XML formatting, and label conventions

Reviewed changes

Copilot reviewed 16 out of 16 changed files in this pull request and generated 2 comments.

Show a summary per file

File	Description
source/main.ptx	Added xi:include statements for 14 modeling sections (c0-c13) before exercises
source/c0-whats-a-de/wad-model.ptx	Newton's cooling model with coffee temperature experiment
source/c1-classification/class-model.ptx	Spring-mass systems demonstrating classification concepts
source/c2-solns/solns-model.ptx	Free fall with air resistance for solution verification
source/c3-di/di-model.ptx	Projectile motion solved by direct integration
source/c4-sov/sov-model.ptx	Logistic population growth with yeast culture experiment
source/c5-if/if-model.ptx	RC circuit charging using integrating factors
source/c6-qm/qm-model.ptx	Harvested fish population with phase line analysis
source/c7-em/em-model.ptx	Nonlinear pendulum for Euler's method
source/c8-lhcc/lhcc-model.ptx	Damped suspension system design
source/c9-uc/uc-model.ptx	Resonance in bridges and buildings with undetermined coefficients
source/c10-lt/lt-model.ptx	Drug dosing and pharmacokinetics using Laplace transforms
source/c11-ltm/ltm-model.ptx	Crash test impact absorption with Laplace transform method
source/c12-ltp/ltp-model.ptx	Thermostat control with piecewise forcing
source/c13-linsys/linsys-model.ptx	Predator-prey dynamics with linear systems
source/c14-nlinsys/nlinsys-model.ptx	SIR epidemic model with nonlinear systems (NOT included in main.ptx)

[geoff-cox]

@copilot apply changes based on the comments in this thread

[Copilot]

@copilot apply changes based on the comments in this thread

The changes from the review comments have already been applied in commits 5f32988 and fc2e42d:

1. Line 80: Corrected matrix element (1,2) from -aR^* to +aR^*
2. Line 105: Corrected matrix A from [[-0.5, -15], [0.25, -15]] to [[-0.5, 15], [0.25, -9]]

Both corrections match the reviewer's suggestions and the mathematics is now consistent with the linearized equations at line 72.