Lectures related to The Mean Value Theorem

Covers Riemann sums, definite integrals, Taylor series, and exponential of complex numbers.

Definite Integrals: Properties and Interpretation

Covers the calculation of minimum points and the concept of definite integrals.

Covers primitive functions, infinite primitives, the theorem on primitives, and examples of indefinite integrals.

Differential Calculation: Hyperbolic Functions

Explores differential calculation with hyperbolic functions and Taylor series, emphasizing the importance of signed areas in integrals.

Fundamental Theorem of Integral Calculus

Explores the fundamental theorem of integral calculus, area calculation, derivatives, and proof techniques.

Integrals of Functions

Covers integrals as the reciprocal function of the derivative and explains displacement integral of velocity and variation of speed and acceleration in rectilinear motion.

Integration Techniques: Part 2

Explores integration techniques, including indefinite integrals and variable changes, through trigonometric functions.

Riemann Integral: Techniques and Fundamentals

Explores Riemann integrability, the fundamental theorem of integral calculus, and various integration techniques.

Fundamental Theorem of Calculus: Integrals and Primitives

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

Taylor Series and Definite Integrals

Explores Taylor series for function approximation and properties of definite integrals, including linearity and symmetry.

Derivative of an Integral with Parameter

Covers deriving integrals with parameters and their derivatives, including special cases and proofs.

Chapter 7: Integral Search for Primitive

Explores primitive functions, their relationship, and techniques for calculating indefinite integrals.

Fundamental Theory of Integral Calculus

Covers the fundamental theory of integral calculus, integration methods, and the importance of finding primitive functions for integration.

Taylor Polynomials and Function Properties

Covers Taylor polynomials, function properties, double integrals, partial derivatives, and function boundaries.

Integral Calculus: Definite and Indefinite Concepts

Covers basic tools for definite integrals, antiderivatives, and integral calculus applications.

Exact Linearization: Earth Dynamics and Stabilization

Explores exact linearization techniques for transforming non-linear systems into linear ones, emphasizing system stability.

Integrals: Indefinite and Definite

Discusses indefinite and definite integrals, their connection, and integration methods.

Integral Calculus: Fundamentals

Covers the fundamentals of integral calculus, including properties of definite integrals and Riemann sums.

Properties of Definite Integrals: Fundamental Theorem of Analysis

Covers the properties of definite integrals and the fundamental theorem of analysis.

Derivative of an Integral

Covers the derivative of an integral dependent on a parameter and its fundamental properties.