Integration by Parts: Techniques and Examples

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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 Coordinate Changes

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

Differentiable Functions: Definitions and Interpretation

Covers the definitions of differentiable and derivable functions and their geometric interpretation.

Functions of Class Ck: Terminology and Definitions

Covers the terminology and definitions of functions of class Ck on real number intervals.

Derivability on an Interval: Rolle's Theorem

Covers derivability on an interval, including Rolle's Theorem and practical applications in function analysis.

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Derivatives of Trigonometric Functions

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

Taylor Series: Analytical Functions

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