Lectures related to Continuous Functions and Elementary Functions

Functions Composition: Continuity & Elements

Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.

Continuous Functions on Open Intervals

Explores continuous functions on open intervals and elementary functions constructed from algebraic functions.

Limits and Operations on Limits

Covers limits, algebraic operations, and infinite limits with examples of functions' behavior near limit points.

Limits and Continuity

Explores limits, continuity, and elementary functions' properties, emphasizing the importance of understanding continuous functions.

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.

Algebraic Identities and Trigonometry

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

Real Functions of Real Variables: Properties and Domains

Covers the properties of real functions, domains, and types of functions, including periodicity.

Trigonometric Equations: Sinus and Cosinus

Covers the resolution of simple trigonometric equations involving sinus and cosinus functions.

Derivatives and Approximations: Logarithmic Functions

Explores derivatives and approximations, focusing on logarithmic functions and their properties.

Derivatives of Trigonometric Inverse Functions

Explores derivatives of trigonometric inverse functions and their properties, with examples and solutions included.

Triangle Resolution: Trigonometric Functions

Covers the resolution of triangles using trigonometric functions and the importance of cosine and sine theorems.

Derivability of Functions

Focuses on determining the derivability of functions within their domains using square roots, logarithmic, and exponential functions.

Trigonometric Formulas: Addition Theorem

Explores trigonometric addition theorem, double angles, and tangent properties.

Generalized Integrals: Convergence and Divergence

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

Symmetries of Trigonometric Functions

Explores the symmetries of trigonometric functions, periodicity, and properties of even and odd functions.

Taylor Polynomials: Approximating Functions

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

Taylor Series: Approximating Functions with Polynomials

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

Rotation of a Vector

Explores the rotation of vectors in a plane using trigonometric functions.

Limits and Continuity: Analysis 1

Explores limits, continuity, and uniform continuity in functions, including properties at specific points and closed intervals.

Trigonometric, Logarithmic and Exponential Functions: Teaser

Explores fundamental special functions with applications in various fields.