Lectures related to Derivability of Functions

Trigonometric Equations: Sinus and Cosinus

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

Implicit Functions Theorem

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Functions: Limits, Continuity, Differentiability

Explores the origin of functions, continuity, differentiability, and the physical representation of chemical bonds.

Advanced Analysis II: Differential Equations and Timers

Discusses advanced analysis concepts, focusing on differential equations and timers in microcontrollers.

Functions Composition: Continuity & Elements

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

Real Numbers and Functions

Introduces Real Analysis I, covering real numbers, functions, limits, derivatives, and integrals.

Bernoulli's Hospital Rule

Covers the statement of the Bernoulli's Hospital Rule and its application.

Calculus: Derivatives and Integrals

Covers the fundamentals of calculus, focusing on derivatives and integrals.

Derivability and Composition

Covers derivability, linear applications, composition of functions, and the gradient vector.

Level Sets and Continuity

Covers level sets and continuity in advanced analysis, emphasizing the importance of understanding level sets for various functions.

Integral Techniques: Integration by Parts

Explores the integration by parts technique through examples, showcasing its step-by-step application to functions like cos(x) and sin(x.

Definitions and Notations

Covers the definitions and notations related to functions.

Advanced Analysis II: Derivatives and Functions

Covers the review of derivatives and functions, including the concept of chain rule and graphical representation.

Implicit Functions Theorem

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Integration by Substitution

Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.

Piecewise Functions Composition

Covers the composition of piecewise functions and introduces the signum and Heaviside functions.

Solutions to QCM 1-3

Covers the solutions to multiple-choice questions 1 to 3.

Applications of Theorems

Demonstrates the practical application of theorems in calculus through two clever examples.

Continuous Functions: Integrability and Examples

Explores continuous functions and integrability through practical examples.