Lectures related to Integration by Parts: Techniques and Examples

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.

Trigonometric Equations: Sinus and Cosinus

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

Continuity of Trigonometric Functions

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

Continuous Functions on Open Intervals

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

Derivatives and Approximations: Logarithmic Functions

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

Trigonometric Formulas: Addition Theorem

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

Cosine Theorem

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

Fourier Series: Convergence and Dirichlet Theorem

Covers Fourier series convergence, Dirichlet theorem, and applications in signal processing.

Symmetries of Trigonometric Functions

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

Integration Techniques: Fundamental Theorems and Methods

Discusses integration techniques, focusing on integration by parts and substitution methods, with practical examples and theoretical insights.

Fundamental Theorem of Calculus: Integrals and Primitives

Explains the Fundamental Theorem of Calculus, focusing on integrals and their relationship with primitives.