This course on Applications of the Derivative aims to teach students how to apply derivatives in various real-world scenarios. By the end of the course, learners will be able to solve problems related to related rates, optimization, differentials, and Taylor polynomials. The course covers topics such as related rates for different scenarios like water flow and speed radar, optimization problems like fence along a river and box with no top, and the use of differentials for error propagation. The teaching method involves a combination of theoretical explanations, examples, and problem-solving exercises. This course is intended for students or individuals studying calculus who want to deepen their understanding of derivatives and their applications in practical situations.
APEX Calculus - Applications of the Derivative
Overview
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.
Taught by
Sean Fitzpatrick
