özel diferansiyel dersi

        DIFFERENTIAL EQUATİONS SUBJECTS

All content in “First order differential equations

Intro to differential equations

• • Differential equation introduction

• • Finding particular linear solution to differential equation

• • Introduction to differential equations and initial value problems

• • Creating a slope field

• • Slope field to visualize solutions

• • Differential equation from slope field

• • Slope fields (Exercise)

Separable equations

• • Separable differential equations introduction

• •  Particular solution to differential equation example  

• • Separable differential equations (Exercise)

• • Old separable differential equations introduction

• • Old separable differential equations example  

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

• • Euler’s Method program code (Scratchpad)

• • Example Euler’s method exercise

• • 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 2  

• • 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

• • Undetermined coefficients 4

 

All content in “Laplace transform”

Laplace transform

• • Laplace transform 1  

• • Laplace transform 2

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

• • Part 2 of the transform of the sin(at)  

Properties of the Laplace transform

• • Laplace as linear operator and Laplace of derivatives (Video)

• • 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