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        Boğaziçi Üniversitesi,İtanbul TEKNİK ÜNİVERSİTESİ,Bilgi Üniversitesi,Koç Üniversitesi,Işık Üniversitesi,  İstanbul Üniversitesi,Yıldız Üniversitesi ,Yeditepe Üniversitesi  Haliç Üniversitesi  Beykent Üniversitesi ,Doğuş Üniversitesi,Kadir  HAS  , Okan  UNİVERSİTESİ,Özyeğin  ÜNİVERSİTESİ, Maltepe  ÜNİVERSİTESİ, Yeni YÜZYİL  ÜN.,ve Kültür Üniversitelerinin ekonomi işletme ,bilgisayar mühendisliği,ekonomi bölümü,insaat mühendisliği ,uluslararasi iliskiler ve  çalışma ekonomisi gibi bölümlerde okuyan onlarca üniversite öğrencisine  özel dersler verdim.          

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