Course content

- The notion of differential equation
- Notation for ODEs
- Order and degree of an ODE
- Solutions of differential equations
- Linear ODEs
- Direction fields
- Euler's method
- Autonomous ODEs
- Existence and uniqueness of solutions of ODEs
- Solution strategy on the basis of the slope field
Separation of variables
- Differentials
- Differential forms and separated variables
- Solving ODEs by separation of variables
Linear first-order differential equations
- Uniqueness of solutions of linear first-order ODEs
- Linear first-order ODE and integrating factor
- Solving linear first-order ODEs
Linear second-order differential equations
- Uniqueness of solutions of linear second-order ODEs
- Homogeneous linear 2nd-order ODEs with constant coefficients
- Solving homogeneous linear 2nd-order ODEs with constant coefficients
- The Ansatz
Solution methods for linear-second order ODEs
- The Wronskian of two differentiable functions
- Variation of constants
- From one to two solutions
- Solving linear second-order ODEs
Systems of differential equations
- Systems of coupled linear first-order ODEs

Differential Equations


Explanations and examples

Unlimited exercises

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Fits well with college STEM courses