Differential equation | 1 Big School (By Blue Brain)

Course Content

First order differential equations

Intro to differential equations
Differential equations introduction
Writing a differential equation
Worked example: linear solution to differential equation
Slope fields
Slope fields introduction
Worked example: equation from slope field
Worked example: slope field from equation
Worked example: forming a slope field
Approximating solution curves in slope fields
Worked example: range of solution curve from slope field
Euler’s Method
Euler’s method
Worked example: Euler’s method
Separable equations
Separable equations introduction
Addressing treating differentials algebraically
Worked example: identifying separable equations
Worked example: finding a specific solution to a separable equation
Worked example: separable equation with an implicit solution
Separable equations (old)
Separable equations example (old)
Exponential models
Exponential models & differential equations (Part 1)
Exponential models & differential equations (Part 2)
Worked example: exponential solution to differential equation
Newton’s Law of Cooling
Worked example: Newton’s law of cooling
Logistic models
Growth models: introduction
The logistic growth model
Logistic equations (Part 1)
Logistic equations (Part 2)
Worked example: logistic model equations
Integrating factors 1
Integrating factors 2
Exact equations and integrating factors
Exact equations intuition 1 (proofy)
Exact equations intuition 2 (proofy)
Exact equations example 1
Exact equations example 2
Exact equations example 3
Homogeneous equations
First order homogenous equations
First order homogeneous equations 2

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 2
Complex roots of the characteristic equations 3
Repeated roots of the characteristic equation
Repeated roots of the characteristic equations part 2
Complex roots of the characteristic equations 1
Method of undetermined coefficients
Undetermined coefficients 1
Undetermined coefficients 2
Undetermined coefficients 3
Undetermined coefficients 4
Laplace transform
Laplace transform 1
Laplace transform 2
L{sin(at)} – transform of sin(at)
Part 2 of the transform of the sin(at)

Laplace transform

Properties of the Laplace transform
Laplace as linear operator and Laplace of derivatives
Laplace transform of cos t and polynomials
“Shifting” transform by multiplying function by exponential
Laplace transform of t: L{t}
Laplace transform of t^n: L{t^n}
Laplace transform of the unit step function
Inverse Laplace examples
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
Laplace/step function differential equation
The convolution integral
Introduction to the convolution
The convolution and the Laplace transform
Using the convolution theorem to solve an initial value prob

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Course Content

First order differential equations

Intro to differential equations

Differential equations introduction

Writing a differential equation

Worked example: linear solution to differential equation

Slope fields

Slope fields introduction

Worked example: equation from slope field

Worked example: slope field from equation

Worked example: forming a slope field

Approximating solution curves in slope fields

Worked example: range of solution curve from slope field

Euler’s Method

Euler’s method

Worked example: Euler’s method

Separable equations

Separable equations introduction

Addressing treating differentials algebraically

Worked example: identifying separable equations

Worked example: finding a specific solution to a separable equation

Worked example: separable equation with an implicit solution

Separable equations (old)

Separable equations example (old)

Exponential models

Exponential models & differential equations (Part 1)

Exponential models & differential equations (Part 2)

Worked example: exponential solution to differential equation

Newton’s Law of Cooling

Worked example: Newton’s law of cooling

Logistic models

Growth models: introduction

The logistic growth model

Logistic equations (Part 1)

Logistic equations (Part 2)

Worked example: logistic model equations

Integrating factors 1

Integrating factors 2

Exact equations and integrating factors

Exact equations intuition 1 (proofy)

Exact equations intuition 2 (proofy)

Exact equations example 1

Exact equations example 2

Exact equations example 3

Homogeneous equations

First order homogenous equations

First order homogeneous equations 2

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 2

Complex roots of the characteristic equations 3

Repeated roots of the characteristic equation

Repeated roots of the characteristic equations part 2

Complex roots of the characteristic equations 1

Method of undetermined coefficients

Undetermined coefficients 1

Undetermined coefficients 2

Undetermined coefficients 3

Undetermined coefficients 4

Laplace transform

Laplace transform 1

Laplace transform 2

L{sin(at)} – transform of sin(at)

Part 2 of the transform of the sin(at)

Laplace transform

Properties of the Laplace transform

Laplace as linear operator and Laplace of derivatives

Laplace transform of cos t and polynomials

“Shifting” transform by multiplying function by exponential

Laplace transform of t: L{t}

Laplace transform of t^n: L{t^n}

Laplace transform of the unit step function

Inverse Laplace examples

Dirac delta function

Laplace transform of the dirac delta function