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All content in “First order differential equations”

Intro to differential equations

• Finding particular linear solution to differential equation
• Introduction to differential equations and initial value problems
• Slope field to visualize solutions
• Differential equation from slope field

Separable equations

• Separable differential equations introduction
• Old separable differential equations introduction

Modeling with differential equations

• Modeling population with simple differential equation
• Particular solution given initial conditions for population
• Newton’s Law of Cooling
•  Applying Newton’s Law of Cooling to warm oatmeal

Logistic differential equation and function

• Modeling population as an exponential function
• Logistic differential equation intuition
• Solving the logistic differential equation part 1
• Solving the logistic differential equation part 2
• Logistic function application

Euler’s Method

• Euler’s method
• Euler’s method program code
• Example Euler’s method exercise

Exact equations and integrating factors

• Exact equations intuition
• Exact equations example
• Exact equations example
• Integrating factors   Homogeneous equations
• First order homogenous equations
• First order homogeneous equations 2

All content in “Second order linear equations”

Linear homogeneous equations

• 2nd order linear homogeneous differential equations 1
• 2nd order linear homogeneous differential equations 2
•  2nd order linear homogeneous differential equations 3
• 2nd order linear homogeneous differential equations 4

Complex and repeated roots of characteristic equation

• Complex roots of the characteristic equations 1
• Complex roots of the characteristic equations 3
• Repeated roots of the characteristic equation
• Repeated roots of the characteristic equations part 2

Method of undetermined coefficients

• Undetermined coefficients 1
• Undetermined coefficients 2
• Undetermined coefficients 3

All content in “Laplace transform”

Laplace transform

• Laplace transform 2
• L{sin(at)}) – transform of sin(at)

Properties of the Laplace transform

• Laplace transform of t^n: L{t^n}
• Laplace transform of the unit step function
• Dirac delta function
• Laplace transform of the dirac delta function

Laplace transform to solve a differential equation

• Laplace transform to solve an equation
• Laplace transform solves an equation 2
• Using the Laplace transform to solve a nonhomogeneous eq

The convolution integral

• Introduction to the convolution