Lectures related to Introduction to Physics: Scientific Approach and Mathematics

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

Introduction: Purpose of Physics, Physical Law, CMS

Introduces the purpose of physics, the role of mathematics, and the importance of observation in understanding natural phenomena.

Warm-up for EPFL: Physics

Offers a warm-up for EPFL students, covering key concepts in mathematics and physics through thematic videos and practical exercises.

Integration Techniques: Fundamental Theorems and Methods

Discusses integration techniques, focusing on integration by parts and substitution methods, with practical examples and theoretical insights.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Differentiability of Functions of Several Variables

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Integration by Substitution

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

Differentiability and Tangent Planes in Multivariable Functions

Covers differentiability in multivariable functions and the existence of tangent planes, emphasizing geometric interpretations and practical applications.

Taylor Polynomials: Approximating Functions in Multiple Variables

Covers Taylor polynomials and their role in approximating functions in multiple variables.

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.

Complex Integration and Cauchy's Theorem

Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.

Improper Integrals: Fundamental Concepts and Examples

Covers improper integrals, their definitions, properties, and examples in two and three dimensions.

Applications of Theorems

Demonstrates the practical application of theorems in calculus through two clever examples.

Mathematics: Cylinders and Parametrizations

Discusses the mathematical concepts of cylinders and their parametrizations, including surface area, volume, and related exercises.

Introduction to Physics: Understanding Natural Phenomena

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

Duplication of the Cube

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

Residue Theorem: Applications in Complex Analysis

Discusses the residue theorem and its applications in calculating complex integrals.

Elliptic Problems

Covers the concept of elliptic problems and their applications in various scenarios.

Green Function and Laplacian Formula

Covers the concept of Green function and Laplacian formulas in mathematics.

Physics Fundamentals: Exploring Scales and Scientific Methods

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