Differential Equations

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Differential Equations

Subjects

  • First Order Differential Equations
    • Linear Equations
    • Nonlinear Equations
    • Separable Equations
    • Exact Solutions
    • Integrating Factors
    • Homogeneous Equations
    • Existence and Uniqueness Theorem
  • Second Order Linear Equations
    • Homogeneous Equations
    • Linear Independence
    • Reduction of Order
    • Homogeneous Equations with Constant Coefficients
    • Complex Roots
    • Method of Underdetermined Coefficients
    • Method of Variation of Parameters
    • Free, Forced Vibrations, Electrical Networks
  • Series solutions for Second-order Equations
  • Higher Order Linear Equations
  • Laplace Transforms
  • Systems of First Order Linear Equations
    • EigenValues and EigenVectors
    • Basic Theory of Systems of Equations
    • Homogeneous Linear Systems with Constant Coefficients
    • Complex eigenvalues
    • Repeated EigenValues
    • Fundamental Matrices
    •  Nonhomogeneous Linear Systems
  • Numerical Methods
  • Nonlinear Differential Equations
  • Partial Differential Equations & Fourier Series
  • Boundry Value Problems and Sturm-Liouville Theory

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