Explore the concept of uniform continuity in real analysis through this 13-minute video lecture. Learn the definition of uniform continuity and how it differs from standard continuity. Examine examples that illustrate these differences, practice proving uniform continuity, and understand why certain functions are not uniformly continuous. Discover two important theorems: one relating to continuous functions on compact sets, and another providing a sequential criterion for non-uniform continuity. Gain insights into enlightening continuity proofs, the uniform continuity of x^2 on compact sets, and the concept of compactness. Access additional resources, including a full real analysis course playlist, exercises, and related proofs to deepen your understanding of this advanced mathematical concept.