APEX Calculus - Applications of the Derivative

Overview

Explore the practical applications of derivatives in calculus through a comprehensive series of video lectures. Delve into related rates problems, optimization techniques, differentials, and Taylor polynomials. Learn to solve real-world scenarios involving changing circumferences, areas, water flow, and speed measurements. Master optimization methods for various geometric and practical situations. Understand the concept of differentials, their applications, and error propagation. Dive deep into Taylor polynomials, including their definition, coefficient determination, and error estimation. Apply these concepts through numerous examples and gain insight into Taylor's Theorem for a well-rounded understanding of derivative applications in calculus.

Syllabus

Derivative Applications: Related Rates - 01. Intro.
Derivative Applications: Related Rates - 02. Circumference.
Derivative Applications: Related Rates - 03. Circle Area.
Derivative Applications: Related Rates - 04. Water Flow.
Derivative Applications: Related Rates - 05. Speed Radar.
Derivative Applications: Related Rates - 06. Turning Camera.
Derivative Applications: Optimization - 01.Product Given Sum.
Derivative Applications: Optimization - 02. Fence Along River.
Derivative Applications: Optimization - 03. Power Line.
Derivative Applications: Optimization - 04. Box With No Top.
Derivative Applications: Differentials - 01. Intro.
Derivative Applications: Differentials - 02. Example.
Derivative Applications: Differentials - 03. Definition.
Derivative Applications: Differentials - 04. Why does dx Equal Delta x.
Derivative Applications: Differentials - 05. Example.
Derivative Applications: Differentials - 06. Example.
Derivative Applications: Differentials - 07. Propagation of Error.
Derivative Applications: Taylor polynomials - 01. Intro.
Derivative Applications: Taylor polynomials - 02. Determining Coefficients.
Derivative Applications: Taylor polynomials - 03. Definition.
Derivative Applications: Taylor polynomials - 04. Example.
Derivative Applications: Taylor polynomials - 05. Example.
Derivative Applications: Taylor polynomials - 06. Example.
Derivative Applications: Taylor polynomials - 07. Taylor's Theorem.
Derivative Applications: Taylor polynomials - 08. Error Estimate Example.
Derivative Applications: Taylor polynomials - 09. Example.