Lectures related to Advanced analysis II: implicit functions theorem

Finding Absolute Extrema in Multivariable Functions

Covers the conditions for finding absolute extrema in multivariable functions.

Real Functions: Definitions and Properties

Covers real functions' definitions, properties, periodicity, and reciprocity, including maximum, minimum, and composition of functions.

Differentiable Functions and Lagrange Multipliers

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

Real Functions: Definitions and Examples

Explores definitions and examples of real functions of a real variable.

Extrema of Functions in Several Variables

Explains extrema of functions in several variables, stationary points, saddle points, and the role of the Hessian matrix.

Extrema of Functions in Several Variables

Explores the conditions for local extrema of functions in several variables, including critical points and the Hessian matrix.

Applications of Differential Calculus

Explores applications of differential calculus, including theorems, convexity, extrema, and inflection points.

Optimization Techniques: Local and Global Extrema

Discusses optimization techniques, focusing on local and global extrema in functions.

Generalized Integrals: Definition and Applications

Covers the definition and applications of generalized integrals in advanced analysis, including real functions, differential equations, and multiple integrals.

Taylor's Formula: Developments and Extrema

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

Local Extrema of Functions

Discusses local extrema of functions in two variables around the point (0,0).

Real Functions: Continuity and Limits

Explores continuity and limits of real functions, including examples and the concept of uniform continuity.

Real Functions: Definitions and Properties

Covers the definitions and basic properties of real functions, including domain, image set, notation, and graph.

Limits of Multivariable Functions: Techniques and Theorems

Discusses limits of multivariable functions, focusing on definitions, examples, and techniques for calculating limits effectively.

Optimization: Local Extrema

Explains how to find local extrema of functions using derivatives and critical points.

Local Extremum Points Determination

Focuses on determining local extremum points of functions through various examples.

Stationary Points: Necessary Conditions and Examples

Covers necessary conditions for extrema and provides illustrative examples.

Differential Equations: Solutions and Periodicity

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Algebraic Identities and Trigonometry

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Real Functions, Continuity, Differential Calculus

Covers real functions, continuity, and differential calculus, including the intermediate value theorem and derivatives.