Differential Equations

Topics covered in a first year course in differential equations.
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Differential Equations

Topics covered in a first year course in differential equations.
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COURSE DESCRIPTION

Topics covered in a first year course in differential equations. Need to understand basic differentiation and integration from Calculus playlist before starting here.
    • Over 45 lectures and 8.5 hours of content!

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CURRICULUM

  • 1
    Introduction to differential equations
    11:02
    What a differential equation is and some terminology.
  • 2
    Separable Differential Equations
    12:00
    Introduction to separable differential equations.
  • 3
    Separable differential equations 2
    05:37
    Another separable differential equation example.
  • 4
    Exact Equations Intuition 1 (proofy)
    09:54
    Chain rule using partial derivatives (not a proof; more intuition).
  • 5
    Exact Equations Intuition 2 (proofy)
    10:51
    More intuitive building blocks for exact equations.
  • 6
    Exact Equations Example 1
    12:09
    First example of solving an exact differential equation.
  • 7
    Exact Equations Example 2
    08:01
    Some more exact equation examples
  • 8
    Exact Equations Example 3
    09:59
    One more exact equation example
  • 9
    Integrating factors 1
    10:16
    Using an integrating factor to make a differential equation exact
  • 10
    Integrating factors 2
    08:26
    Now that we've made the equation exact, let's solve it!
  • 11
    First order homegenous equations
    07:21
    Introduction to first order homogenous equations.
  • 12
    First order homogenous equations 2
    08:22
    Another example of using substitution to solve a first order homogeneous differential equations.
  • 13
    2nd Order Linear Homogeneous Differential Equations 1
    09:44
    Introduction to 2nd order, linear, homogeneous differential equations with constant coefficients.
  • 14
    2nd Order Linear Homogeneous Differential Equations 2
    08:28
    Let's find the general solution!
  • 15
    2nd Order Linear Homogeneous Differential Equations 3
    05:59
    Let's use some initial conditions to solve for the particular solution
  • 16
    2nd Order Linear Homogeneous Differential Equations 4
    09:10
    Another example with initial conditions!
  • 17
    Complex roots of the characteristic equations 1
    10:27
    What happens when the characteristic equations has complex roots?!
  • 18
    Complex roots of the characteristic equations 2
    10:23
    What happens when the characteristic equation has complex roots?
  • 19
    Complex roots of the characteristic equations 3
    10:12
    Lets do an example with initial conditions!
  • 20
    Repeated roots of the characteristic equation
    11:58
    What happens when the characteristic equation only has 1 repeated root?
  • 21
    Repeated roots of the characterisitic equations part 2
    08:52
    An example where we use initial conditions to solve a repeated-roots differential equation.
  • 22
    Undetermined Coefficients 1
    10:11
    Using the method of undetermined coefficients to solve nonhomogeneous linear differential equations.
  • 23
    Undetermined Coefficients 2
    11:00
    Another example using undetermined coefficients.
  • 24
    Undetermined Coefficients 3
    08:09
    Another example where the nonhomogeneous part is a polynomial
  • 25
    Undetermined Coefficients 4
    05:54
    Putting it all together!
  • 26
    Laplace Transform 1
    08:01
    Introduction to the Laplace Transform
  • 27
    Laplace Transform 2
    07:34
    Laplace transform of e^at
  • 28
    Laplace Transform 3 (L{sin(at)})
    10:44
    Laplace Transform of sin(at) (part 1)
  • 29
    Laplace Transform 4
    09:13
    Part 2 of getting the Laplace transform of sin(at)
  • 30
    Laplace Transform 5
    11:36
    Useful properties of the Laplace Transform
  • 31
    Laplace Transform 6
    09:45
    Laplace transform of cosine and polynomials!
  • 32
    Laplace Transform to solve an equation
    10:51
    Using the Laplace Transform to solve an equation we already knew how to solve.
  • 33
    Laplace Transform solves an equation 2
    10:46
    Second part of using the Laplace Transform to solve a differential equation.
  • 34
    More Laplace Transform tools
    11:17
    A grab bag of things to know about the Laplace Transform.
  • 35
    Using the Laplace Transform to solve a nonhomogenous eq
    18:48
    Solving a non-homogeneous differential equation using the Laplace Transform
  • 36
    Laplace Transform of : L{t}
    09:06
    Determining the Laplace Transform of t
  • 37
    Laplace Transform of t^n: L{t^n}
    10:16
    Laplace Transform of t^n: L{t^n}
  • 38
    Laplace Transform of the Unit Step Function
    24:15
    Introduction to the unit step function and its Laplace Transform
  • 39
    Inverse Laplace Examples
    19:15
    Using our toolkit to take some inverse Laplace Transforms
  • 40
    Laplace/Step Function Differential Equation
    19:12
    Hairy differential equation involving a step function that we use the Laplace Transform to solve.
  • 41
    Dirac Delta Function
    17:48
    Introduction to the Dirac Delta Function
  • 42
    Laplace Transform of the Dirac Delta Function
    12:13
    Figuring out the Laplace Transform of the Dirac Delta Function
  • 43
    Introduction to the Convolution
    18:59
    Introduction to the Convolution
  • 44
    The Convolution and the Laplace Transform
    13:46
    Understanding how the product of the Transforms of two functions relates to their convolution.
  • 45
    Using the Convolution Theorem to Solve an Initial Value Prob
    12:14
    Using the Convolution Theorem to solve an initial value problem

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