Lectures related to Introduction: Purpose of Physics, Physical Law, CMS

Introduction to Physics: Scientific Approach and Mathematics

Covers the scientific method, mathematical descriptions, and the role of mathematics in Physics.

Introduction to Physics: Understanding Natural Phenomena

Covers the basics of physics, emphasizing understanding natural phenomena and the role of mathematics in representing physical laws.

The Fourth Pillar of Culture: Informatics

Explores informatics as the fourth pillar of culture, its evolution, integration into society, and applications in modern physics and mathematics.

Physics Fundamentals: Exploring Scales and Scientific Methods

Covers the fundamental concepts of physics, emphasizing scientific methods and measurement across various spatial scales.

Advanced Physics I: Introduction to Mechanics

Introduces the basics of physics, including mechanics and making predictions based on observations and hypotheses.

Sets and Operations: Introduction to Mathematics

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Metaphysics: Aristotle's Theory and Natural Philosophy

Explores Aristotle's metaphysics, the role of science in answering 'why' questions, and the essence of natural philosophy.

Linear Algebra: Injective Functions

Explores injective functions in linear algebra, demonstrating how to prove injectivity step by step.

Complex Numbers: Introduction and Operations

Covers the introduction and operations of complex numbers in physics and engineering applications.

Derivative of an Integral with Parameter

Covers deriving integrals with parameters and their derivatives, including special cases and proofs.

Optimal Transport: From Theory to Applications

Explores the history, theory, and applications of optimal transport in various fields, showcasing its importance in solving complex mathematical problems.

Dirac Delta Function

Introduces the Dirac delta function and discusses its properties and applications in signal processing and physics.

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Integration by Substitution

Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.

Duplication of the Cube

Delves into the historical challenge of duplicating the cube, exploring construction methods, misattributions, and geometric concepts.

Implicit Functions Theorem

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Calculus of Variations: Gradient Young Theorem

Covers the Gradient Young Theorem in the calculus of variations, discussing proofs and applications.

Supremum Theorem

Explores the Supremum Theorem, its properties, proofs, and exercises.

Lagrange Theorem: Applications and Proofs

Covers the application and proof of the Lagrange theorem in group theory.

The Intermediate Value Theorem

Explains the Intermediate Value Theorem for continuous functions on closed intervals.