Lectures related to Derivatives and Trigonometry Fundamentals

Differential Calculation: Trigonometric Derivatives

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

Fundamental Theorem of Calculus: Integrals and Primitives

Explains the Fundamental Theorem of Calculus, focusing on integrals and their relationship with primitives.

Explores limits, continuity, and function compositions in mathematics.

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

Circular Motion in a Train: Mechanics

Explores circular motion in a train, discussing position, velocity, and acceleration in different frames of reference.

Trigonometric Equations: Sinus and Cosinus

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

Triangle Resolution: Trigonometric Functions

Covers the resolution of triangles using trigonometric functions and the importance of cosine and sine theorems.

Derivatives of Trigonometric Inverse Functions

Explores derivatives of trigonometric inverse functions and their properties, with examples and solutions included.

Taylor Polynomials: Calculating Limits and Derivatives

Covers the calculation of Taylor polynomials and their applications in limits and derivatives of functions from R² to R.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Circular Motion and Harmonic Oscillator

Explores circular motion, harmonic oscillators, and double springs, elucidating the physics principles behind them.

Complex Numbers: Introduction and Operations

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

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.

Trigonometric Functions: Basics and Applications

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

Cosine Theorem

Explores the cosine theorem in triangles, analyzing side and angle relationships.

Trigonometric Functions: Right Triangle

Introduces trigonometric functions in right triangles, exploring angles, ratios, and special values.

Trigonometric Functions: Sin and Cos

Covers the definition of sine and cosine functions, their graphs, and notable points.

Trigonometric Circle: Interpretation and Applications

Explores the interpretation of angles on the trigonometric circle and its applications in circular motion.

Taylor Polynomials: Approximating Functions in Multiple Variables

Covers Taylor polynomials and their role in approximating functions in multiple variables.

Taylor Development: Higher Derivatives

Covers the calculation of Taylor polynomials, higher derivatives, and Taylor series using examples.