Lectures related to Continuity in Analysis

Differentiating under the integral sign

Explores differentiating under the integral sign and continuity of functions in integrals.

Real Functions: Definitions and Properties

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

Continuity and Limits

Explores continuity and limits, emphasizing their relationship and practical applications in function analysis.

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.

Partial Derivatives: Definitions and Examples

Covers the concept of partial derivatives and their applications in mathematical analysis.

Analysis I: Intermediate Value Theorem

Covers the Intermediate Value Theorem, functions' properties, continuity, finding roots, and differentiation concepts.

Limits of Functions

Explores the existence of limits of functions under specific conditions.

Distribution & Interpolation Spaces

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

Theorems in Analysis

Covers the Meyers-Serrin theorem in analysis, discussing the conditions for functions in different spaces.

Functions: Limits, Continuity, Differentiability

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

Study of Convergence in Analysis I

Covers the study of convergence of sequences, integrals, and functions.

Definitions and Notations

Covers the definitions and notations related to functions.

Convergence in Analysis III

Covers the concept of convergence in Analysis III, focusing on normal convergence and convergence in a specific form.

Advanced Analysis: Differential Equations Overview

Provides an overview of differential equations, their properties, and methods for finding solutions through various examples and graphical representations.

Analysis IV: Convolution and Partial Derivatives

Covers the properties of functions in Rn and the computation of partial derivatives by induction.

Distributed Computation I

Explores distributed computation between two parties in a distant setting.

Derivability and Continuity

Explores derivability and continuity of functions, showcasing examples of functions with differentiability properties.

Advanced Analysis II: Cauchy Problem and Differential Equations

Covers the Cauchy problem in differential equations, focusing on initial conditions and their impact on solution uniqueness.

Understanding Microcontrollers: Functions

Introduces the fundamentals of functions in microcontroller programming, emphasizing naming rules and step-by-step development.

Advanced Analysis II: Gradient Generalizations

Explores gradient generalizations and applications in advanced analysis.