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APEX Calculus - Integration

Sean Fitzpatrick via YouTube

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Overview

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This course develops integral calculus through antiderivatives, definite and Riemann integrals, the Fundamental Theorem of Calculus, area between curves, average value, initial value problems, and substitution.

Syllabus

Integration: Antiderivatives - 01. Intro.
Integration: Antiderivatives - 02. Definition and Indefinite Integrals.
Integration: Antiderivatives - 03. Example.
Integration: Antiderivatives - 04. Example.
Integration: Antiderivatives - 05. Initial Value Problems.
Integration: Antiderivatives - 06. Example.
Integration: Antiderivatives - 07. Example.
Integration: Definite - 01. Intro.
Integration: Definite - 02. Example with Velocity.
Integration: Definite - 03. Definition.
Integration: Definite - 04. Example.
Integration: Definite - 05. Properties.
Integration: Definite - 06. Geometric Examples.
Integration: Definite - 07. Example.
Integration: Riemann - 01. Introduction.
Integration: Riemann - 02. Approximation.
Integration: Riemann - 03. Summation Notation.
Integration: Riemann - 04. Summation Examples.
Integration: Riemann - 05. Summation Properties.
Integration: Riemann - 06. Partitions.
Integration: Riemann - 07. Example.
Integration: Riemann - 08. Definition.
Integration: Riemann - 09. Example.
Integration: Riemann - 10. Example with n Rectangles.
Integration: Riemann - 11. Example With Limit.
Integration: Riemann - 12. Limit of Riemann sum gives definite integral.
Integration: FTC - 01. Intro.
Integration: FTC - 02. Example.
Integration: FTC - 03. FTC Part I.
Integration: FTC - 04. Example.
Integration: FTC - 05. FTC Part II.
Integration: FTC - 06. Proof.
Integration: FTC - 07. Example.
Integration: FTC - 08. Examples.
Integration: FTC - 09. FTC and Chain Rule.
Integration: FTC - 10. Examples.
Integration: FTC - 11. Area Between Curves.
Integration: FTC - 12. Example.
Integration: FTC - 13. Example.
Integration: FTC - 14. MVT for Integrals.
Integration: FTC - 15. Average Value.
Techniques of Integration: Substitution - 01. Intro.
Techniques of Integration: Substitution - 02. Definite integrals.
Techniques of Integration: Substitution - 03. Examples.
Techniques of Integration: Substitution - 04. Example.
Techniques of Integration: Substitution - 05. Examples.
Techniques of Integration: Substitution - 06. Trig Examples.
Techniques of Integration: Substitution - 07. Definite Integral Example.

Taught by

Sean Fitzpatrick

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