Course info
This course provides a comprehensive introduction to the theory and applications of ordinary differential equations (ODEs) and partial differential equations (PDEs), which are fundamental tools for modeling and solving problems in science, engineering, and applied mathematics.
The first part of the course focuses on ordinary differential equations, including classification by order and degree, formation of differential equations, and solution techniques for first-order equations such as separable, linear, exact, and Bernoulli equations. Higher-order linear differential equations with constant coefficients are also studied, along with methods like undetermined coefficients and variation of parameters. Applications in physical systems such as growth and decay, mechanical vibrations, and electrical circuits are emphasized.
The second part introduces partial differential equations, covering basic concepts, formation, and classification. Standard methods for solving first-order PDEs (such as Lagrange’s method) and second-order PDEs are discussed. The course also includes classical equations like the wave equation, heat equation, and Laplace’s equation, along with techniques such as separation of variables and Fourier series methods.
By the end of the course, students will be able to:
Classify and solve various types of ODEs and PDEs
Apply analytical methods to real-world problems
Interpret the physical meaning of solutions
Develop mathematical models using differential equations
This course builds a strong foundation for advanced studies in applied mathematics, engineering analysis, and computational modeling.
The first part of the course focuses on ordinary differential equations, including classification by order and degree, formation of differential equations, and solution techniques for first-order equations such as separable, linear, exact, and Bernoulli equations. Higher-order linear differential equations with constant coefficients are also studied, along with methods like undetermined coefficients and variation of parameters. Applications in physical systems such as growth and decay, mechanical vibrations, and electrical circuits are emphasized.
The second part introduces partial differential equations, covering basic concepts, formation, and classification. Standard methods for solving first-order PDEs (such as Lagrange’s method) and second-order PDEs are discussed. The course also includes classical equations like the wave equation, heat equation, and Laplace’s equation, along with techniques such as separation of variables and Fourier series methods.
By the end of the course, students will be able to:
Classify and solve various types of ODEs and PDEs
Apply analytical methods to real-world problems
Interpret the physical meaning of solutions
Develop mathematical models using differential equations
This course builds a strong foundation for advanced studies in applied mathematics, engineering analysis, and computational modeling.
- Teacher: Anwar Ahmad Siddiquee