Lectures related to Brook Taylor

Functions: Differentials, Taylor Expansions, Integrals

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

Taylor Series: Cosine Function

Explains the Taylor series expansion of order 4 for the cosine function.

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Integration Techniques: Series and Functions

Covers integration techniques for series and functions, including power series and piecewise functions.

Taylor Series: Order 4

Covers the Taylor series of order 4 and its applications in trigonometric functions.

Generalized Integral: Comparison Criteria and Taylor Series

Explores series convergence criteria, generalized integrals, and Taylor series applications.

Integration of CnR Class Functions

Explains the integration of Taylor series for CnR class functions.

Differential Calculation: Hyperbolic Functions

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

Taylor Series: Derivatives and Integrals

Explores Taylor series expansions for derivatives and integrals, with a focus on multiple derivatives and error terms.

Taylor Series: Convergence and Applications

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

Taylor Series: Analytical Functions

Explores Taylor series, radius of convergence, and analytical trigonometric functions.

Power series and Taylor series

Covers the properties of improper integrals, power series, and Taylor series.

Q&A Session: System Design, Law of Motion, Parasitic Blade Movement

Covers system design, law of motion, and parasitic blade movement.

Calculating with Taylor, Convexity

Covers calculating with Taylor series and convexity concepts, including sin(x) and cos(x) approximations.

Real Analysis: Summary

Covers real numbers, sequences, series, functions, limits, derivatives, Taylor series, integrals, and more.

Approximating Functions with Taylor Series

Explores approximating functions with Taylor series, showcasing step-by-step calculations and practical applications.

Mathematical Reminders: Derivatives, Primitives, Integrals

Covers mathematical reminders on derivatives, primitives, and integrals, including common functions and Taylor series expansions.

Taylor Development: Higher Derivatives

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

Analyse I: Summary

Covers real numbers, complex numbers, numerical sequences, series, real functions, function limits, derivatives, Taylor series, integrals, and growth rates of functions.

Derivatives of Entire Functions

Explores derivatives of entire functions and the use of Taylor series for function representation.