It emphasizes intuitive, practical and computational approaches, while also covering necessary proofs and demonstrations. The goal is to bring the material to life by seamlessly integrating mathematics with its physical applications. Concepts and methods are presented based on their relevance to physics, with examples and problems drawn from both classical and modern physics. Excessive formalism, which tends to hide the true nature of physical problems and the most appropriate way of approaching them, has been kept to a minimum. Instead, I have endeavored to highlight, as far as possible, the "underlying ideas" of the various mathematical procedures and methods. The course will include seven units presented with a cohesive formalism, emphasizing underlying unity and common themes wherever possible. They are: 1) Vector spaces and linear algebra, 2) Curvilinear coordinates, 3)Differential and integral operators, 4) Variational calculus, 5) Function spaces and orthogonal polynomials, 6) Differential equations, ordinary and partial, 7) Green's function.
