This video answers the following questions: What are differential equations? What does it mean if a function is a solution of a differential equation? Why ar...
I present the existence and uniqueness theorem for first-order ordinary differential equations. For an introduction to differential equations, see my video: ...
An introduction to theoretical mathematics via the basic concepts of analysis: fields, the real numbers, least upper bounds, the limit, sequences, Cauchy seq...
Principles of Mathematical Analysis (based on Rudin's book of that name, Chapters 1, 2, 4, 5, 3, 7). (Prerequisites: some familiarity with theoretical mathem...
Mathematics as a Non-Superstition. Eleven math courses (in the playlists), from high school (precalculus) to early graduate school (functional analysis), taught in such a way that the student should be able to defend (almost) all statements against objection.
Playlist List (sorted by last added):
Course 4: Linear Algebra
Course 3: Calculus II (US)
Course 2: Calculus I (Another extra)
Course 7: Principles of Mathematical Analysis
Course 9: Basic Functional and Harmonic Analysis
Course 8: Fourier Analysis
Course 8: Complex Analysis
Course 6: Introduction to Analysis
Course 5: Differential Equations
Course 4: Multivariable Calculus
Course 3: Calculus II
Course 2: Calculus I
Course 1: Precalculus
This series of 5 videos will provide an introduction to geometric calculus for those who know some vector calculus. It is based on my textbook "Vector and Ge...