Approximation Techniques in Multivariable Functions

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Functions and Derivatives

Explores continuity, differentiability, boundedness, and extrema of functions in multiple variables.

Taylor Series: Approximating Functions with Polynomials

Explores approximating functions with polynomials using Taylor series and discusses the convergence of series representations.

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.

Intersection Numbers: Algebraic Counting Solutions

Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.

Taylor Approximation: Matrix and Polynomials

Explores Taylor approximation of functions using polynomials and matrices for quadratic approximation.

Implicit Functions and Taylor Polynomials

Covers implicit functions, Taylor polynomials, and tangent equations.

Calculus Foundations: Taylor Series and Integrals

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

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Differentiable Functions and Lagrange Multipliers

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