The course follows the book *Differential Equations with Boundary-Value Problems* by D. G. Zill, and W. S. Wright, 8th Ed, Cengage Learning, 2012

The other usefull sources, which were helpful to prepare my notes:

By *Miroslav Stibor*, Zaman University. You can get all the below chapters in one PDF (5 MB):

# List of chapters

### First order DE

- Introduction to differential equations
- Solution by separating variables
- Solution of linear DE
- Solution of exact (total) DE
- Solution by substitution
- Homogeneous DE
- Bernoulli DE

- Numerical method to solve first order DE (Euler's method)

### Modeling with first order DE

- Real-world problems modeling with first order DE

### Higher order DE

- Introduction to higher order linear DE
- Homogeneous linear DE
- Reduction of order method (for higher order linear DE with non-constant coefficients)
- Homogeneous linear DE with constant coefficients

- Nonhomogeneous linear DE with constant coefficients: Undetermined coefficients to find $y_p()$
- Undetermined coefficients—Superposition approach
- Undetermined coefficients—Annihilator approach

- Variation of parameters method to find $y_p()$ from $y_c()$
- Cauchy-Euler equation (a special type of linear DE with non-constant coefficients)
- System of linear DE with constant coefficients (by means of operator $D$)
- Nonlinear DE of higher order (substitution $u=y'$, Taylor series)

### Modeling with higher order DE

- Linear models, initial value problems
- Linear models, boundary value problems
- Nonlinear models

### Series solution of DE

- Power series
- Power series at singular points

### The Laplace Transform

- Definition of the Laplace Transform
- Solving DE with the Laplace Transform
- Additional properties and operations
- Solving partial DE using Laplace transform

### Fourier series

- Introduction to Fourier series
- Solving DE by Fourier series
- Fourier transform

### Partial differential equations, boundary value problems

- Problems from physics
- Separable partial differential equation