Taylor Polynomials: Approximating Functions in Multiple Variables

Related lectures (16)

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

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

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

Discusses the Taylor series and secant method, focusing on their applications in numerical analysis and root-finding techniques.

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

Covers numerical methods for root finding, focusing on the secant and Newton's methods.

Introduces calculus concepts, focusing on Taylor series and integrals, including their applications and significance in mathematical analysis.

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

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

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