Taylor Series: Analytical Functions

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Functions and Coordinate Changes

Explores bijective functions, coordinate transformations, and graphical representations in two dimensions.

Nth Derivative

Explores obtaining n-th derivatives through a recursive process and the regularity of functions defined by power series.

Trigonometric Equations: Sinus and Cosinus

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

Taylor Series: Convergence and Applications

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

Functions Composition: Continuity & Elements

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

Trigonometric Formulas: Addition Theorem

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

Derivatives of Trigonometric Functions

Explores the derivatives of trigonometric functions and their geometric interpretations, including sine, cosine, and tangent functions.

Complex Analysis: Laurent Series and Residue Theorem

Discusses Laurent series and the residue theorem in complex analysis, focusing on singularities and their applications in evaluating complex integrals.

Trigonometric Functions: Sin and Cos

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

Differentiability and Tangent Planes

Explores differentiability in functions and geometric interpretation of tangent planes.