Differential Equations curriculum & tutors

Math

An ordinary differential equations path covering modeling, first-order methods, qualitative analysis, second-order systems, Laplace transforms, numerical methods, and applications.

8 public curriculum units1 tutor availableAlways Free
College bridge / first-year undergraduate

Differential Equations curriculum

An ordinary differential equations path covering modeling, first-order methods, qualitative analysis, second-order systems, Laplace transforms, numerical methods, and applications.

Pacing
8 units, 20-30 weeks self-paced
Units
8 unit sequence
Practice
640 checked answers
Support
Self-paced or tutor-guided
Outcomes
  • Model changing systems with differential equations and stated assumptions.
  • Solve first-order, second-order, and systems problems using appropriate methods.
  • Use qualitative and numerical tools when closed forms are unavailable or misleading.

Video companion links

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Unit sequence

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  1. 01

    Modeling with differential equations

    • Translate rates, stocks, forces, and constraints into equations.
    • Check units, variables, parameters, and initial conditions.

    Practice: Turn a physical or population scenario into an ODE model and name every assumption.

  2. 02

    First-order equations

    • Solve separable, linear, exact, and substitution-based first-order ODEs.
    • Use initial conditions and domains carefully.

    Practice: Solve three first-order equations and classify the method used for each.

  3. 03

    Autonomous equations and qualitative analysis

    • Use equilibria, phase lines, stability, and slope fields.
    • Predict long-run behavior without solving explicitly.

    Practice: Create a phase-line analysis for a logistic-style model and explain stability.

  4. 04

    Linear second-order equations

    • Solve homogeneous and forced equations with constant coefficients.
    • Interpret natural frequency, damping, resonance, and transients.

    Practice: Model a spring-mass system and classify underdamped, critically damped, or overdamped behavior.

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