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MATH-505In Development

Calculus & University Mathematics

Differential Equations and Mathematical Modeling

Model dynamic systems with first- and higher-order differential equations, qualitative analysis, and numerical approximations.

Level
Level 5 — Higher Mathematics
Learning time
20 hours
Format
Extended Course
Modules
10

Course structure

A clear outline before lessons begin.

This course is published as a development map. Full lessons, practice, and assessments will be added after content review.

Prerequisites

Complete these courses before beginning when they are available.

Recommended preparation

These courses strengthen preparation but are not strict prerequisites.

Learning outcomes

By the end, learners will be able to…

  • Formulate differential-equation models from changing quantities and assumptions.
  • Solve common first-order differential equations analytically.
  • Solve introductory higher-order linear differential equations.
  • Analyze equilibrium, stability, and long-term behavior of simple systems.
  • Use transform or numerical methods when an exact solution is impractical.
  • Interpret a model’s assumptions, units, and limitations.

Module outline preview

10 planned modules

Estimated times add up to the course’s planned learning time. Every module is in development.

  1. 01

    Modeling Change with Differential Equations

    Translate a rate relationship into a differential equation and initial condition.

    2 hours · In Development
  2. 02

    Separable First-Order Equations

    Solve and interpret models that separate variables.

    2 hours · In Development
  3. 03

    Linear First-Order Equations

    Use integrating factors to solve non-separable linear models.

    2 hours · In Development
  4. 04

    Qualitative Analysis and Equilibria

    Analyze direction fields, equilibrium points, and stability.

    2 hours · In Development
  5. 05

    Systems of Differential Equations

    Represent linked changing quantities and interpret system behavior.

    2 hours · In Development
  6. 06

    Higher-Order Homogeneous Equations

    Solve constant-coefficient second-order models.

    2 hours · In Development
  7. 07

    Forced Equations and Response Models

    Analyze nonhomogeneous behavior in applied systems.

    2 hours · In Development
  8. 08

    Laplace-Transform Methods

    Use transform reasoning for selected initial-value problems.

    2 hours · In Development
  9. 09

    Numerical Solution Methods

    Approximate solutions and evaluate step-size error.

    2 hours · In Development
  10. 10

    Modeling Synthesis

    Compare solution methods and communicate the scope of a dynamic model.

    2 hours · In Development

Course status

Course coming soon

This course is not yet open for enrollment and does not include lessons, practice, assessments, or formal credit. You can review the outline while it is developed.

Back to Mathematics

Recommended learning paths

A clear sequence, not a random list.

These paths show a recommended order. Branches identify connected study that can follow once prerequisites are complete.