Lectures related to Taylor Series: Order 4

Taylor Development: Convexity

Covers the Taylor development theorem, convexity, and computation rules with Taylor.

Taylor Development: Higher Derivatives

Covers the calculation of Taylor polynomials, higher derivatives, and Taylor series using examples.

Limits and Operations on Limits

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

Trigonometric Equations: Sinus and Cosinus

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

Trigonometric Formulas: Addition Theorem

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

Continuity of Trigonometric Functions

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

Taylor Series: Analytical Functions

Explores Taylor series, radius of convergence, and analytical trigonometric functions.

Trigonometric Functions: Sin and Cos

Covers the definition of sine and cosine functions, their graphs, and notable points.

Symmetries of Trigonometric Functions

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

Harmonic Oscillations: Superposition

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

Triangle Resolution: Trigonometric Functions

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

Cosine Theorem

Explores the cosine theorem in triangles, analyzing side and angle relationships.

Functions Composition: Continuity & Elements

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

Function Approximation: Order 5

Illustrates the calculation of a fifth-order Taylor expansion around zero for a given function.

Trigonometric Formulas: Bisection & Transformations

Covers trigonometric bisection formulas and transformations between sums and products.

Derivatives of Trigonometric Inverse Functions

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

Trigonometric Functions: Tangent and Cotangent

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

Reciprocal Trigonometric Functions

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

Trigonometric Functions: Basics and Applications

Introduces the basics of trigonometric functions, their properties, and practical applications in geometry and physics.

Trigonometric Equations: Basics

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