Explore advanced analytical and numerical methods for solving partial differential equations in this comprehensive lecture delivered by Oscar Reula from the National University of Córdoba, Argentina. Develop expertise in mathematical techniques essential for understanding complex physical phenomena through rigorous theoretical frameworks and computational approaches. Master both classical analytical solutions and modern numerical methods used in contemporary research applications. Gain insights from an expert perspective on the interplay between theoretical mathematics and practical problem-solving in the field of partial differential equations. Build foundational knowledge that bridges pure mathematics with applied sciences, preparing you for advanced research or professional applications requiring sophisticated mathematical modeling skills.