Differential equations for college and university students. Contains direction fields, separation of variables, linear 1st & 2nd order ODEs, LaPlace transforms, and more.

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- Introduction to differential equations
- The notion of differential equations
- Notation for ODEs
- Order and degree of an ODE
- Solution of differential equations
- Linear ODEs

- Direction field
- Direction field
- 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 2nd-order ODEs
- Homogeneous linear 2nd-order ODEs with constant coefficients
- Solving homogeneous linear 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

- End of differential equations
- Applications of ODEs

- Differential equations and Laplace transforms
- The Laplace transform
- The inverse Laplace transform
- Laplace transforms of differential equations
- Convolution
- Laplace transforms of heaviside functions
- Laplace transforms of periodic functions
- Riemann-Stieltjes intergration
- Laplace transforms of delta functions
- Transfer and response functions