Lectures related to Analyse I IN/SC: Improper Integrals and Real Functions

Transforms of the Place

Explores the intuition behind transforms of the place and addresses audience questions on integral calculations and function choices.

Introduction to Mathematics for Engineers

Introduces the purpose of mastering mathematics and calculation tools for engineers, emphasizing the need to think methodically and rigorously.

Real Functions: Definitions and Examples

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

Real Analysis: Summary

Covers real numbers, sequences, series, functions, limits, derivatives, Taylor series, integrals, and more.

Real Functions: Definitions and Graphs

Covers real functions, definitions, graphs, parity, periodicity, and boundedness.

Taylor Polynomials and Function Properties

Covers Taylor polynomials, function properties, double integrals, partial derivatives, and function boundaries.

Curve Length and Function Definition

Explores curve length, function definition, continuity, derivatives, integrals, and graphical representations of functions in two variables.

Algebraic Identities and Trigonometry

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

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.

Taylor Polynomials: Approximating Functions

Introduces Taylor polynomials for approximating functions around a point, showcasing their importance in accurately representing 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.

Functions: Differentials, Taylor Expansions, Integrals

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

Real Functions: Continuity and Limits

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

Mathematics: Analysis and Algebra Overview

Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.

Taylor Polynomials: Approximation and Integration

Covers Taylor polynomials for approximation and indefinite integrals of elementary functions.

Differential Equations: Solutions and Periodicity

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

Taylor Polynomial in Two Variables

Covers the Taylor polynomial in two variables and the concept of extrema in functions of several variables.

Lagrangian Multipliers: Extrema and Constraints

Covers Lagrangian multipliers, extrema with constraints, multiple integrals, and Darboux sums.

Real Functions: Composition and Limits

Explores real functions, composition, and limits, including algebraic operations and sequence characterization.

Real Functions: Continuity

Covers the concept of real functions, focusing on continuity and the behavior of polynomials and ratios of polynomials.