Derivatives of Functions

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Related lectures (23)

Derivatives and Trigonometry Fundamentals MOOC: Warm-up for EPFL

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

Developing Limit Concepts

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

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.

Taylor Polynomial: Order 2

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

Integrals of Functions MOOC: Warm-up for EPFL

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

Applications of Theorems

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

Taylor's Formula: Developments and Extrema

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

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Mechanics: Introduction and Calculus Log in to Mediaspace to watch this video

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

Taylor Polynomials: Calculating Limits and Derivatives Log in to Mediaspace to watch this video

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

Calculus: Derivatives and Integrals Log in to Mediaspace to watch this video

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

Implicit Functions Theorem Log in to Mediaspace to watch this video

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

Laplacian in Polar and Spherical Coordinates: Derivatives Log in to Mediaspace to watch this video

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

Integration by Substitution Log in to Mediaspace to watch this video

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

CMS - Physique (Burmeister): Mouvement Log in to Mediaspace to watch this video

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

Advanced Physics I: Trajectory and Velocity Log in to Mediaspace to watch this video

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

Taylor Polynomials: Approximating Functions in Multiple Variables Log in to Mediaspace to watch this video

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

Differential Calculus: Definition and Derivability Log in to Mediaspace to watch this video

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

Functions: Differentials, Taylor Expansions, Integrals Log in to Mediaspace to watch this video

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

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