Math 527 Additional Summer Resources

First order equations: 

• Separable Equations

  • Paul
  • Organic Chemistry Tutor

• Linear First-Order Equations (integrating factor)

  • Paul
  • Organic Chemistry Tutor

• Exact Equations

  • Paul
  • Khan Academy

• Substitutions

  • Algebraically Homogeneous
    • Paul
      (note: he uses a slightly different notation to determine homogeneity)
    • Organic Chemistry Tutor
      (note: he does not give criteria for making this substitution)
  • Bernoulli
    • Paul
    • Organic Chemistry Tutor

Second order equations: 

• Linear independence and the Wronskian

  • Paul
  • More Paul

• Second order constant coefficient problems

  • Homogeneous 
    • Case 1: Real Distinct Roots
      • Paul
    • Case 2: Real Repeated Roots
      • Paul
    • Case 3: Complex Roots
      • Paul
    • All: Organic Chemistry
  • Non-homogeneous
    • Method of Undetermined Coefficients
      • Paul
      • Organic Chemistry Tutor
    • Variation of Parameters
      • Paul
      • Organic Chemistry Tutor
        (note: both use different notation. Compare with your class notes for consistent use)

• Higher order constant coefficient equations

Laplace transforms: 

• By definition

  • ​​​​​​​Paul
  • Dr. Trefor Bazett

• Using the table

  • ​​​​​​​Paul

• Inverse transforms: 

  • ​​​​​​​Paul 

• Solving ODEs via Laplace Transforms

  • ​​​​​​​Paul 
  • Dr. Trefor Bazett

• Unit step function and delta distribution

  • ​​​​​​​Paul
  • Paul again
  • Paul

Dr. Trefor Bazett's full Laplace playlist 

Systems of odes: 

• Systems of equations

  • ​​​​​​​Paul
  • Paul on matrices
  • Jeffrey Chasnov
    (note: he does not explain the "why", if you are interested)

• Eigenvalues/eigenvectors

  • ​​​​​​​Paul

• Solutions by eigenvalue/eigenvector

  • ​​​​​​​Case 1: real distinct eigenvalues
    • ​​​​​​​Paul 
    • Jeffrey Chasnov
  • Case 2: (may get to) repeated eigenvalues
    • ​​​​​​​Paul
  • Case 3: complex eigenvalues
    • ​​​​​​​Paul 
    • Jeffrey Chasnov