3 Credit hours (3 h lectures). This course aims to provide a comprehensive foundation in differential equations: It covers first-order equations (separable and linear) and second-order equations (homogeneous and non-homogeneous), as well as partial differential equations such as the heat, diffusion, and wave equations in nanoscale systems. Boundary value problems, and analytical methods including separation of variables, Laplace transforms, and Laplace transforms. Also, in matrix algebra: determinants and inverse matrices, eigenvalues and eigenvectors, matrix decomposition, and systems of linear equations.
Course objectives:
1. Understand and classify ordinary and partial differential equations, including first-order, second-order, and classical PDEs relevant to physical and engineering systems.
2. Apply analytical solution techniques such as separation of variables, Laplace transforms, and Laplace transforms to solve initial and boundary value problems.
3. Formulate and solve partial differential equations governing heat, diffusion, and wave phenomena, with emphasis on applications in nanoscale systems.
4. Analyze and solve systems of linear equations using matrix algebra methods, including determinants and inverse matrices.
5. Compute and interpret eigenvalues and eigenvectors, and apply matrix decomposition techniques to coupled systems and differential equations.
6. Develop mathematical modeling, analytical reasoning, and problem-solving skills applicable to advanced studies and applications in science, engineering, and nanotechnology.