Block I

Introduction to DEs

Linear Homogeneous DEs

Block II

Linear Non-homogeneous DEs

Introduction to Laplace Transforms

Block III

More Laplace Transforms

Systems of DEs, Basic Matrix Theory

Block IV

Eigenvalues/vectors, Fourier Series,

PDEs/Heat Equation

1.1 Definitions and Terminology

1.2 Initial Value Problems

2.1 Direction Fields and Isoclines

2.2 Separable DEs

2.3 1st Order Linear DEs

2.6 Euler's Method

3.1a Applications of 1st Order DEs

3.1b Chemical Mixing Problems

4.1 Basic Theory of IVPs

4.3a Homogeneous Linear DEs (Real Roots)

4.3b Homogeneous Liner DEs (Complex Roots)

5.1.1 Mass Spring Systems (Free/Undamped)

5.1.2 Mass Spring Systems (Free/Damped)

4.4 Undetermined Coefficients (Examples)

5.1.3 Mass Spring Systems (Driven Motion)

5.1.4 Electric Circuits

7.1 Laplace Transforms

7.2.1 Inverse Laplace Transforms

7.2.2 Laplace Transforms of Derivatives

7.3.1 1st Translation Theorem/Completing the Square

7.3.2 2nd Translation Theorem/Unit Step Functions

7.4 Derivatives/Convolutions

7.5 Dirac Delta Function

7.5H Green's Function/Impulse Response (Handout)

AII.1 Matrix Theory (no Inverse)

AII.2 Gaussian Elimination

7.6 Systems of DEs by Laplace Transforms

7.6b Coupled Springs

7.6c Electrical Networks (more notes)

AII.4 Eigenvalues/vectors (2x2 Matrices)

8.1 Systems of DEs in Matrix From

8.2.1 Distinct Real Eigenvalues

9.4 Euler's Method for Systems

11.2 Fourier Series

11.3 Odd/Even Function, Sin/Cos Series

12.1 PDEs, Separation of Variables

12.3a Heat Equation (0 Temp Ends)

12.3b Heat Equation (Insulated Ends)