Lectures related to Convex Functions: Theorems and Examples

Advanced Analysis: Differential Equations Overview

Covers the fundamentals of differential equations, their properties, and methods for finding solutions through various examples.

Real Numbers and Functions

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

Implicit Functions Theorem

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

Applications of Theorems

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

Convex Functions

Covers the properties and operations of convex functions.

Bernoulli's Hospital Rule

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

Advanced Analysis II: Derivatives and Functions

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

Integration by Substitution

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

Taylor's Formula: Developments and Extrema

Covers Taylor's formula, developments, and extrema of functions, discussing convexity and concavity.

Calculus: Derivatives and Integrals

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

Introduction to Mathematics for Engineers

Introduces the purpose of mastering mathematics and calculation tools for engineers, emphasizing the need to think methodically and rigorously.

Differential Equations: Solutions and Monotonicity

Explores solutions of differential equations and their monotonicity properties.

Taylor Polynomial: Order 2

Presents the solution to finding the second-order Taylor polynomial of a function.

Linear Independence: The Wronskian Concept

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

Linear Independence: The Wronskian Concept

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

Advanced Analysis: Differential Equations Overview

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

Real Analysis: Basics and Sequences

Introduces real analysis basics, including functions, sequences, limits, and set properties in R.

Analysis I: Limits and Continuity

Covers the concepts of limits and continuity, focusing on the demonstration of various theorems.

Sequences and Convergence: Understanding Mathematical Foundations

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Laplacian in Polar and Spherical Coordinates: Derivatives

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.