Following are some course lecture notes written for the [MAT219]
Introduction to Differential Equations course taught at METU Cyprus.
The course uses Boyce and DiPrima's differential equations book, but
is reorganized so that "Systems of Differential Equations" (Ch 7)
is taught in the first part of the course --
**before** "High Order Linear" (Ch 3-4).

Since students were having trouble with "Systems of DE", I wrote up some
(mostly) clean course notes for distribution and extra study. *There are
a few places with computational errors in these notes.* I also included
notes connecting to the "High Order Linear" chapters (3-4) because we organized
our work there differently than Boyce and DiPrima. Also included are some
extra notes reviewing Laplace transforms (Chapter 6).

The rough course outline is presented below. Sections without uploaded
notes are written in ~~strikeout~~.

~~Directional Fields~~- Separable Equations and "Homogeneous Separable" .
~~Linear Equations~~

Integrating Factors and Variation of Parameters~~Modeling~~~~Existence and Uniqueness Theorems~~- Exact Equations .

- Introduction .
- Basic Theory .
- Basic Examples .
- Real and Complex Eigenvalue Cases .
- More Complex Eigenvalue Examples .
- Review of Systems so Far .
- Fundamental Matrix Notation (Matrix Exponentiation) .
- Generalized Eigenvectors (Jordan Form) Part I .
- Generalized Eigenvectors (Jordan Form) Part II .
- Variation of Parameters (2x2 and 3x3) .

- Deriving Higher Order Linear from Systems (2 lectures).
- Undetermined Coefficients for Higher Order Linear .
- Variation of Parameters for 2nd Order Linear .
~~Vibrations~~(see Course Summary Sheet)

~~Laplace Transform Basics~~~~Step Functions and Differential Equations~~~~Impulse Functions and Differential Equations~~~~Convolutions and Green's Function (Impulse Response)~~

~~Derivation of Heat Conduction Equation; Boundary Value Problems~~~~Fourier Series~~~~Fourier Series of Even and Odd Extensions~~

(*Sine*and*Cosine*Series)~~Separation of Variables; Solution to Heat Equation~~