Oxford Calculus - Partial Differentiation, Critical Points, PDEs, and Fourier Series

Learn advanced calculus concepts through a comprehensive video series taught by University of Oxford mathematician Dr. Tom Crawford, covering essential topics from the Oxford mathematics curriculum. Master partial differentiation techniques and discover how to find and classify critical points for functions of two variables using discriminant analysis. Explore three-dimensional mathematical visualization through plotting 3D graphs and calculating divergence, while developing proficiency in solving differential equations using integrating factors and separation of variables methods. Delve into partial differential equations (PDEs) including simple solving techniques and separable solutions, with particular focus on deriving and solving the fundamental heat equation. Understand advanced mathematical concepts including Jacobians, Taylor's theorem with complete derivation and practical examples, and Fourier series development. Build expertise in vector calculus operations, specifically gradient (grad) and divergence (div) calculations, while working through numerous examples that demonstrate real-world applications of these mathematical principles in university-level mathematics.