Differential Equations curriculum

Start with 18.03 Differential Equations and Calculus textbooks. Take notes until you can explain: Translate rates, stocks, forces, and constraints into equations.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Turn a physical or population scenario into an ODE model and name every assumption.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Check units, variables, parameters, and initial conditions.

Start with 18.03 Differential Equations and Calculus textbooks. Take notes until you can explain: Solve separable, linear, exact, and substitution-based first-order ODEs.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Solve three first-order equations and classify the method used for each.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Use initial conditions and domains carefully.

Start with 18.03 Differential Equations and Calculus textbooks. Take notes until you can explain: Use equilibria, phase lines, stability, and slope fields.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Create a phase-line analysis for a logistic-style model and explain stability.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Predict long-run behavior without solving explicitly.

Start with 18.03 Differential Equations and Calculus textbooks. Take notes until you can explain: Solve homogeneous and forced equations with constant coefficients.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Model a spring-mass system and classify underdamped, critically damped, or overdamped behavior.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Interpret natural frequency, damping, resonance, and transients.

Start with 18.03 Differential Equations and Calculus textbooks. Take notes until you can explain: Convert higher-order equations into systems.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Sketch a phase portrait from trace, determinant, and eigenvalue information.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Use eigenvalues and eigenvectors to analyze linear systems.

Start with 18.03 Differential Equations and Calculus textbooks. Take notes until you can explain: Use transforms for initial-value problems.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Solve an IVP with a step input and interpret the result in time.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Handle step functions, impulses, and discontinuous forcing.

Start with 18.03 Differential Equations and Calculus textbooks. Take notes until you can explain: Approximate solutions using Euler, improved Euler, Runge-Kutta, and series ideas.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Compare Euler and Runge-Kutta approximations against a known solution.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Estimate numerical error and stability limits.

Start with 18.03 Differential Equations and Calculus textbooks. Take notes until you can explain: Model circuits, mixing, epidemics, mechanics, and coupled systems.

Do the first sequenced checks until the definitions, vocabulary, and setup are correct without hints.

Produce the assignment artifact, then pass the application and analysis checks tied to: Build a full ODE case study with model, solution method, validation, and sensitivity check.

Any miss becomes an error-log entry, a clean redo, and one nearby transfer problem before advancing.

Bring your attempted work, the exact missed check, and one question about: Communicate model limits honestly.