Differential equations
Undergraduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Differential Equations — scope drawn from OpenStax Calculus Volume 2 (intro DE) and Volume 3 (second-order DE), plus typical US ODE course syllabi.
First-order equations
- Classification of ODEs — Classification of ODEs
- Existence (informal) — Existence (informal)
- Direction fields — Direction fields
- Euler's method for first-order equations — Euler's method for first-order equations
- Separable differential equations — Separable differential equations
- First-order linear equations — First-order linear equations; integrating factors
- Exact equations — Exact equations
- Integrating factors (where covered) — Integrating factors (where covered)
- Substitution methods — Substitution methods
- Bernoulli equations (optional) — Bernoulli equations (optional)
- Modeling with first-order equations — Modeling with first-order equations
- Newton's law of cooling — Newton's law of cooling
Second-order linear equations
- Second-order linear homogeneous equations with constant coefficients — Second-order linear homogeneous equations with constant coefficients
- Characteristic equations — Characteristic equations
- Complex roots — Complex roots
- Nonhomogeneous equations — Nonhomogeneous equations; method of undetermined coefficients
- Variation of parameters for second-order equations — Variation of parameters for second-order equations
Laplace transforms and systems
- Laplace transforms — Laplace transforms
- Shifting theorems — Shifting theorems
- Solving IVPs with Laplace transforms — Solving IVPs with Laplace transforms
- Partial fractions — Partial fractions
- Systems of first-order linear equations and matrix methods (introduction) — Systems of first-order linear equations and matrix methods (introduction)
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- First-order equations
Classification of ODEs
Coming soon - Second-order linear equations
Second-order linear homogeneous equations with constant coefficients
Coming soon - Laplace transforms and systems
Laplace transforms
Coming soon
Notes
Undergraduate Differential Equations — scope drawn from OpenStax Calculus Volume 2 (intro DE) and Volume 3 (second-order DE), plus typical US ODE course syllabi. Topic outline: `content/topics/undergraduate/diff_eq.json`.