Lectures related to Derivatives of Functions

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

Derivatives and Trigonometry Fundamentals

Introduces derivatives, trigonometry, and motion principles through basic and trigonometric functions differentiation.

Explores developing limits using Taylor series for function approximations and understanding functions with derivatives approaching zero.

Taylor Polynomials: Calculating Limits and Derivatives

Covers the calculation of Taylor polynomials and their applications in limits and derivatives of functions from R² to R.

Mathematical Reminders: Derivatives, Primitives, Integrals

Covers mathematical reminders on derivatives, primitives, and integrals, including common functions and Taylor series expansions.

Implicit Functions and Taylor Polynomials

Covers implicit functions, Taylor polynomials, and tangent equations.

Calculus: Derivatives and Integrals

Covers the fundamentals of calculus, focusing on derivatives and integrals.

Taylor Polynomial: Order 2

Presents the solution to finding the second-order Taylor polynomial of a function.

Implicit Functions Theorem

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Integrals of Functions

Covers integrals as the reciprocal function of the derivative and explains displacement integral of velocity and variation of speed and acceleration in rectilinear motion.

Laplacian in Polar and Spherical Coordinates: Derivatives

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Integration by Substitution

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

Applications of Theorems

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

CMS - Physique (Burmeister): Mouvement

Explains velocity, acceleration, and displacement in physics, emphasizing precision and direction in movement.

Advanced Physics I: Trajectory and Velocity

Explores trajectory, velocity, and acceleration in advanced physics, emphasizing rectilinear motion and the importance of instantaneous velocity.

Taylor Polynomials: Approximating Functions in Multiple Variables

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

Differential Calculus: Definition and Derivability

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

Taylor's Formula: Developments and Extrema

Covers Taylor's formula, developments, and extrema of functions, discussing convexity and concavity.

Functions: Differentials, Taylor Expansions, Integrals

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

Advanced Physics I

Covers definitions, vectors, motion, speed, acceleration, and derivatives in advanced physics.