Catholic Tech

Differential Equations

Course Topics

  1. Unit 1: Introduction to Differential Equations
    • Overview of differential equations
    • Basic definitions and concepts
    • Classification of differential equations
    • Initial value problems and boundary value problems
  2. Unit 2: First-Order Differential Equations
    • Separable equations
    • Linear equations
    • Exact equations
    • Integrating factors
    • Applications of first-order equations
  3. Unit 3: Second-Order Linear Equations
    • Homogeneous equations
    • Constant coefficient equations
    • Fundamental solutions and the Wronskian
    • Method of undetermined coefficients
    • Variation of parameters
    • Applications of second-order equations
  4. Unit 4: Systems of Differential Equations
    • Introduction to systems of equations
    • Matrix notation and basic operations
    • Eigenvalues and eigenvectors
    • Homogeneous linear systems
    • Nonhomogeneous linear systems
    • Applications of systems of equations
  5. Unit 5: Laplace Transforms
    • Definition and properties of Laplace transforms
    • Laplace transform of derivatives and integrals
    • Inverse Laplace transforms
    • Solving differential equations using Laplace transforms
    • Convolution theorem and applications
  6. Unit 6: Power Series Solutions
    • Power series representation of functions
    • Taylor series expansions
    • Solutions of differential equations as power series
    • Ordinary points and singular points
    • Frobenius method
    • Bessel's equation and Bessel functions
  7. Unit 7: Applications of Differential Equations
    • Vibrations and resonance
    • Electrical circuits
    • Population dynamics
    • Heat conduction
    • Fluid flow
    • Other selected applications

Disclaimer

The course syllabus is subject to change at the discretion of the instructor. Any modifications or updates will be communicated in advance.