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DİFFERANSİYEL ÖZEL DERS

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