Differential Equations
Course Topics
- 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
- Unit 2: First-Order Differential Equations
- Separable equations
- Linear equations
- Exact equations
- Integrating factors
- Applications of first-order equations
- 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
- 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
- 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
- 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
- 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.