Introduction to Differential Equations

Introduction to Differential Equations (David Polletta, 23:36)

Solution to some Differential Equations (David Polletta, 32:16)

Equilibrium Solutions and Stability Example (Paul Vaz, 4:38)

Classification of Differential Equations (David Polletta, 34:41)

Classification of Differential Equations Examples (Paul Vaz, 2:49)

Exponential Function Example (Katie Kolossa, 1:31)

Sine Function Example (Katie Kolossa, 1:37)

First Order Differential Equations

Method of Integrating Factors (David Polletta, 23:33)

Linear, 1st Order Example (Katie Kolossa, 3:33)

Linear, 1st Order Example (Katie Kolossa, 4:26)

Separable Equations (David Polletta, 33:47)

Initial Value Problem Example (Katie Kolossa, 1:33)

Implicit Solution Example (Katie Kolossa, 2:04)

Implicit Solution Example (Katie Kolossa, 3:21)

Modeling with First order equations (David Polletta, 34:41)

Modeling First Order Equations (Paul Vaz, 20:19)

Newton's Law Example (Katie Kolossa, 3:57)

Water Tank Example (Katie Kolossa, 5:16)

Equation of a Curve Example (Katie Kolossa, 1:21)

Population of an Organism Example (Katie Kolossa, 4:54)

Difference Between Linear and Nonlinear Equations (David Polletta, 45:27)

Autonomous Equations and Population Dynamics (David Polletta, 32:12)

Inflection Points (David Polletta, 29:03)

Euler’s Method (David Polletta, 38:34 )

Second Order Differential Equations

Second Order Differential Equations (Rochus Boerner, 27:19)

2nd Order Constant Coefficients Example (Katie Kolossa, 1:44)

Existence and Uniqueness for Linear 2nd order ODEs (Rochus Boerner, 27:21)

Fundamental sets and the Wronskian (David Polletta, 42:20)

Complex Characteristic Roots (Rochus Boerner, 23:25)

Initial Conditions not at t=0 Example (Katie Kolossa, 5:57)

3rd Order Constant Coefficients Example (Katie Kolossa, 4:27)

Repeated Roots and Reduction of Order (Rochus Boerner, 21:48)

4th Order Constant Coefficients Example (Katie Kolossa, 5:15)

Match Third Order Equations Example (Katie Kolossa, 5:33)

The Method of Undetermined Coefficients for Nonhomogenous ODE's (Rochus Boerner, 33:44)

Particular Solution of Sin and Cos Function Example (Katie Kolossa, 3:43)

Exponential (Ate^bt) Forcing Function Example (Katie Kolossa, 3:33)

Forcing Function is not Linearly Independent of the Complementary Solution (Katie Kolossa, 4:16)

Mechanical and Electrical Vibrations (Rochus Boerner, 19:48)

Forced Vibrations (Rochus Boerner, 23:47)

Mass Spring System I - Forced Vibration (Paul Vaz, 2:36)

Mass Spring System II - Forced Vibration (Paul Vaz, 2:30)

Mass Spring System III - Forced Vibration (Paul Vaz, 6:40)

The Laplace Transform

Laplace Transform (David Polletta, 36:19)

Algebra of Laplace Transform (David Polletta, 19:49)

Inverse Laplace Transform (Scott Surgent, 6:08)

Laplace Transform for Solving Differential Equations (Scott Surgent, 7:50)

Laplace Transform of derivative and initial value problem (David Polletta, 33:54)

Step Functions (David Polletta, 23:16)

Laplace Transform of Unit Step function (David Polletta, 18:06)

IVPs with discontinuous forcing functions (David Polletta, 32:46)

Delta Function (David Polletta, 32:28)

Systems of Linear Differential Equations

System of First Order Linear Equations (David Polletta, 26:15)

Solving Homogeneous Linear Systems with Constant Coefficients: Real Distinct Eigenvalues (David Polletta, 18:44)

Geometry of Solutions (David Polletta, 18:01)

Solving Homogeneous Linear Systems with Constant Coefficients: Complex Eigenvalues (David Polletta, 21:00)

Example application (David Polletta, 17:22)

Phase shift and arctan of two arguments (David Polletta, 35:21)

Supplementary materials: Some Linear Algebra concepts (David Polletta, 25:11)