Lectures related to Mathematical Functions: Theory and Applications

Algebraic Identities and Trigonometry

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

Harmonic Oscillations: Superposition

Explores the principle of superposition for harmonic oscillations and provides geometric interpretations and examples.

Trigonometric Formulas: Addition Theorem

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

Integration Techniques: Part 2

Explores integration techniques, including indefinite integrals and variable changes, through trigonometric functions.

Continuity of Trigonometric Functions

Explores the continuity of trigonometric functions and demonstrates specific limits and propositions related to them.

Functions Composition: Continuity & Elements

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

Functions and Periodicity

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

Reciprocal Trigonometric Functions

Explores reciprocal trigonometric functions, hyperbolic functions, and area theorems.

Trigonometric Functions: Right Triangle

Introduces trigonometric functions in right triangles, exploring angles, ratios, and special values.

Triangle Resolution: Trigonometric Functions

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

Derivatives of Trigonometric Inverse Functions

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

Trigonometric Equations: Basics

Introduces the basics of solving trigonometric equations through examples and various techniques.

Symmetries of Trigonometric Functions

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

Differentiable Functions and Lagrange Multipliers

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

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.

Trigonometric Functions: Tangent and Cotangent

Explores the definition, properties, and geometric interpretations of tangent and cotangent functions in trigonometry.

Fresnel Integrals: Curvilinear Integrals in R^2

Explores Fresnel integrals through curvilinear integrals in R^2, focusing on cos(x²-y) and sin(x) functions.

Trigonometric Formulas: Bisection & Transformations

Covers trigonometric bisection formulas and transformations between sums and products.

Trigonometric Equations: Sinus and Cosinus

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

Transformations: Expressing Sums and Products

Covers expressing sums and products using trigonometric functions step by step.