Lectures related to Function Composition

Algebraic Identities and Trigonometry

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Composition of Functions: Application and Reciprocal Functions

Covers the composition of functions and reciprocal functions, with examples and formulas on logarithms and bijective functions.

Linear Algebra: Properties of Injective and Surjective Functions

Covers the properties of injective and surjective functions and the concept of bijections.

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Derivatives and Function Composition

Covers derivatives rules and function composition with examples and explanations.

Function Composition and Limits

Covers function composition, limits, bijective functions, and the characterization of limits using sequences.

Functions Composition: Continuity & Elements

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

Advanced Analysis II: Derivatives and Notations

Covers derivatives, notations, composition of functions, and multiple derivatives in advanced analysis.

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Linear Algebra: Injective Functions

Explores injective functions in linear algebra, demonstrating how to prove injectivity step by step.

Linear Algebra: Injections, Surjections, Bijections

Explores injections, surjections, and bijections in linear algebra, highlighting their significance in mathematics.

Advanced Analysis II: General Variable Change

Explores general variable change in advanced analysis with practical examples.

Inverse Functions: Guided Exercises

Covers guided exercises on inverse functions and the composition of functions.

Derivatives of Functions

Introduces derivatives, composition of functions, Taylor expansion, velocity, acceleration, and temporal derivative notation in physics.

Real Numbers and Functions

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

Differential Equations: Implicit Function Theorem Applications

Discusses the reduction of higher-order differential equations to first-order systems using the implicit function theorem.

Change of Coordinates: Analysis Week 8

Explores changing coordinates, bijective functions, Jacobian matrices, and reciprocal functions in analysis.

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Inverse Function Identity

Explains the inverse function identity and provides examples with ln(x), sin(x), and cos(x).

Linear Algebra: Surjections and Bijections

Explains surjections and bijections in linear algebra, focusing on function properties and inverse identification.