## Topics for the 2nd midterm

Chapter 4: Second order ODEs
- solutions of homogeneous ODEs e.g. y'' - 6y'' + 8y = 0
- particular solutions of inhomoegeneous ODEs e.g. y'' - 2y' + 3y = cos t
- finding particular solutions of inhomogeneous ODEs using variation of parameters method

Chapter 5: Laplace transform
- Definition and properties of Laplace transform e.g. L(e^{at} f) = F(s-a)
- Using Laplace transform to solve ODEs
- Calculating the inverse Laplace transform (there are some techniques)

Chapter 7: Linear algebra
- Basic concepts of vector spaces, matrices and linear maps e.g. how are linear maps and matrices related?
- Multiplication of matrices
- Solving simple systems of linear equations by reducing to row-echelon form