Lectures related to Lagrangian Multipliers: Extrema and Constraints

Generalized Integrals: Definition and Applications

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

Multiple Integrals: Definitions and Properties

Covers the definition and properties of multiple integrals, including double and triple integrals.

Curve Length and Function Definition

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

Fubini's Theorem: Multiple Integrals

Explores Fubini's Theorem for multiple integrals, emphasizing the n=2 case.

Introduction to Mathematics for Engineers

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

Double Integrals: Definitions and Properties

Covers the definitions and properties of double integrals over compact regions.

Analyse I IN/SC: Improper Integrals and Real Functions

Covers improper integrals, study of functions, Taylor polynomials, and real numbers.

Definite Integrals: Properties and Interpretation

Covers the calculation of minimum points and the concept of definite integrals.

Multiple Integrals: Defining Integrals of Functions in R^2

Covers the definition of double integrals for functions of two variables over a domain in the plane R^2.

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Real Functions: Definitions and Examples

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

Real Functions: Definitions and Graphs

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

Real Analysis: Summary

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

Green's Functions in Laplace Equations

Covers the concept of Green's functions in Laplace equations and their solution construction process.

Magnetostatics: Magnetic Field and Force

Covers magnetic fields, Ampère's law, and magnetic dipoles with examples and illustrations.

Advanced analysis II: jordan-measurable sets

Explores Jordan-measurable sets and their properties, including volume calculations and change of variables in integrals.

Taylor Series and Definite Integrals

Explores Taylor series for function approximation and properties of definite integrals, including linearity and symmetry.

Fubini Theorem on Closed Rectangles

Explores the Fubini theorem on closed rectangles in R², discussing integrability, iterated integrals, and compact sets.

Generalized Integrals: Convergence and Divergence

Explores the convergence and divergence of generalized integrals using comparison methods and variable transformations.

Comparison Series and Integrals

Explores the relationship between series and integrals, highlighting convergence criteria and function examples.