Lectures related to Limit Theorems: Two Gendarmes Theorem

Integration Techniques: Fundamental Theorems and Methods

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

Trigonometric Functions: Basics and Applications

Introduces the basics of trigonometric functions, their properties, and practical applications in geometry and physics.

Trigonometric Equations: Sinus and Cosinus

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

Derivatives and Trigonometry Fundamentals

Introduces derivatives, trigonometry, and motion principles through basic and trigonometric functions differentiation.

Trigonometric Formulas

Covers examples of trigonometric, logarithmic, and exponential functions, focusing on solving equations and applying trigonometric identities.

Differential Calculation: Trigonometric Derivatives

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

Applications: Trigonometric Functions

Explores applications of trigonometric functions, focusing on the tangent function and its derivatives.

Prelude: Linking Mathematics and Course Content

Introduces the course content by linking familiar mathematics with upcoming topics.

Applications of Theorems

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

Advanced Analysis II: Variation of Constants Method

Covers the variation of constants method for solving first-order linear differential equations, detailing its steps and implications for general and particular solutions.

Introduction to Mathematical Concepts

Introduces fundamental mathematical concepts and their applications in equations and inequalities.

Calculus: Derivatives and Integrals

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

Integration by Substitution

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

Mathematics: Limits and Trigonometric Functions

Explores limits in mathematics, focusing on trigonometric functions and algebraic transformations to evaluate them.

Complex Numbers: Introduction and Operations

Covers the introduction and operations of complex numbers in physics and engineering applications.

Integral Calculus: Review and Examples

Covers a review of integral calculus concepts and provides examples of solving integrals.

Improper Integrals: Fundamental Concepts and Examples

Covers improper integrals, their definitions, properties, and examples in two and three dimensions.

Elementary Functions: Examples

Covers elementary functions like sin(x), cos(x), and tan(x) with examples and properties.

Limits Analysis

Explores the analysis of limits in different mathematical cases using trigonometry and polar coordinates.

Sequences and Convergence: Understanding Mathematical Foundations

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