Lectures related to Advanced Physics I: Orders of Magnitude

Introduces the fundamentals of advanced physics, emphasizing mechanics and historical developments from Aristotle to Newton.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Covers the kinematics of a material point, including orders of magnitude and practical applications.

Explores Newton's laws of motion, fundamental forces in nature, and the unification of interactions.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Explores angular momentum, central forces, and gravitational theory, including Kepler's laws and Newton's approach.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Covers one-dimensional and two-dimensional motion, dynamics, and energy with a focus on mathematical modeling and rigorous approach.

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Explores Newton's laws of motion, covering inertia, force, acceleration, action, reaction, frames of reference, and measurement of force.

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.

Explores material and energy balances in chemical engineering for process optimization and design.

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Explores convolution, uniform continuity, Hilbert structure, and Lebesgue measure in analysis.