Standard syllabus
Differential equations · Undergraduate · Math
Learning objectives from the Differential equations syllabus, grouped by unit. Click an objective for study materials.
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)
Learning objectives
Click an objective for study materials.
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)
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 (introduct... — Systems of first-order linear equations and matrix methods (introduction)
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
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
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$1,162 · Differential equations · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle.