Ordinary Differential Equations

Text Book : –

Advanced Engineering Mathematics 5th Edition  [ Download ]

Course Description : –

This course provides an introduction to topics involving ordinary differential equations.
Emphasis is placed on the development of abstract concepts and applications for first-order and linear higher-order differential equations, systems of differential equations, numerical methods, series solutions, eigenvalues and eigenvectors, and LaPlace transforms. Upon completion, students will be able to demonstrate understanding of the theoretical concepts and select and use appropriate models and techniques for finding solutions to differential equations-related problems with and without technology.

  • Introduction to Differential Equations .
    • 1.1: Definitions and Terminology .
    • 1.2: order and degree .
  • First-Order Differential Equations .
    • 2.1: Variable Separable Equations .
    • 2.2: Integrating Factor .
    • 2.3: Linear Equation .
    • 2.4: Exact Equations .
    • 2.5: Homogenious ODE .
    • 2.6: Bernoulli Equation .
    • 2.7: Recatti Equation .
    • 2.8: Solutions by Substitutions .
  • Higher – Order Differential Equations .
    • 3.1: Theory of Linear Equations .
      • 3.1.1: Initial-value and boundary-Value Problems .
      • 3.1.2: Homogeneous Equations .
      • 3.1.3: Nonhomogeneous Equations .
    • 3.2: Reduction of Order .
    • 3.3: Homogeneous Linear Equations with Constant Coefficients .
    • 3.4: Undetermined Coefficients .
    • 3.5: Variation of Parameters .
    • 3.6: Cauchy-Euler Equations .
  • The Laplace Transform .
    • 4.1: Definition of the Laplace Transform .
    • 4.2: The Inverse Transform and Transforms of Derivatives .
      • 4.2.1: Inverse Transforms .
      • 4.2.2: Transforms of Derivatives .
  • Series solutions of linear differential equations .
    • 5.1: Series Solution of ODE .