Differential Equations

Course content

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

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