math 228 umich

Exponential Growth and0:05:30

Exponential Growth and Decay

Convolution and the0:05:57

Convolution and the Laplace Transform

The Dirac Delta0:07:14

The Dirac Delta Function

The Laplace Transform0:06:36

The Laplace Transform of Translations

The Convolution of0:05:54

The Convolution of Two Functions

Constant Coefficient ODEs0:07:21

Constant Coefficient ODEs with the Rational Root Theorem: Example 1

An Initial Value0:04:44

An Initial Value Problem with Multiple Delta Forcings

Power Series Solutions0:12:55

Power Series Solutions to Linear Differential Equations: Proof of Analyticity

The Laplace Transform:0:05:46

The Laplace Transform: An Example

Writing a Piecewise0:02:55

Writing a Piecewise Function with the Heaviside Function

Constant Coefficient ODEs0:04:38

Constant Coefficient ODEs with the Rational Root Theorem: Example 3

Laplace Transforms0:08:03

Laplace Transforms

Inverse Laplace Transform0:05:18

Inverse Laplace Transform with Convolution

Inverse Laplace Transforms0:06:02

Inverse Laplace Transforms The Series Method

Solving an Integral0:06:27

Solving an Integral Equation with Laplace Transform Example 1

Autonomous ODEs Example0:05:29

Autonomous ODEs Example 1

Constant Coefficient ODEs:0:04:17

Constant Coefficient ODEs: Example 1 with Repeated Complex Roots

Homogeneous Differential Equations0:07:52

Homogeneous Differential Equations

Inverse Laplace Transforms0:05:05

Inverse Laplace Transforms with Series: An Example

An Impulse Response0:05:56

An Impulse Response Equation

Constant Coefficient ODEs0:06:05

Constant Coefficient ODEs with the Rational Root Theorem: Example 2

Inverse Laplace Transforms0:05:24

Inverse Laplace Transforms with Partial Fractions: Example 1

The Laplace Transform0:05:19

The Laplace Transform and Initial Value Problem: An Nonhomogeneous Example

Solving Initial Value0:06:48

Solving Initial Value Problems with the Laplace Transform