Standard syllabus
Differential equations · Undergraduate · Math
Topics
First-order equations
- Classification of ODEs; initial value problems and existence (informal)
- Direction fields and Euler's method for first-order equations
- Separable differential equations
- First-order linear equations; integrating factors
- Exact equations and integrating factors (where covered)
- Substitution methods and Bernoulli equations (optional)
- Modeling with first-order equations: growth/decay, mixing, and Newton's law of cooling
Second-order linear equations
- Second-order linear homogeneous equations with constant coefficients
- Characteristic equations; distinct, repeated, and complex roots
- Nonhomogeneous equations; method of undetermined coefficients
- Variation of parameters for second-order equations
Laplace transforms and systems
- Laplace transforms: definition, tables, and shifting theorems
- Solving IVPs with Laplace transforms and partial fractions
- Systems of first-order linear equations and matrix methods (introduction)
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$1,162 · Differential equations · 18 tutoring hrs
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