23MAT103-DIFFERENTIAL EQUATIONS AND TRANSFORMS

This course provides a comprehensive introduction to the theory and applications of differential equations and integral transforms, which are fundamental tools in engineering and applied sciences. It focuses on developing analytical and problem-solving skills required to model and solve real-world problems.

The course begins with first-order differential equations, including methods such as variable separable, exact equations, and linear differential equations. It then extends to higher-order linear differential equations with constant coefficients, covering both homogeneous and non-homogeneous cases along with particular integrals.

Further, the course introduces partial differential equations, emphasizing formation, classification, and solution techniques for first-order equations. Applications in physical systems such as heat conduction, wave motion, and engineering processes are highlighted.

A significant portion of the course is dedicated to integral transforms, particularly the Laplace Transform and Fourier Series. Students will learn how these transforms simplify differential equations into algebraic forms, making them easier to solve. Concepts such as inverse transforms, convolution theorem, and applications in solving initial and boundary value problems are also covered.

By the end of the course, students will be able to formulate mathematical models using differential equations, apply appropriate solution techniques, and use transforms to analyze complex engineering systems efficiently.