This course on Integration covers topics such as antiderivatives, definite integrals, Riemann sums, the Fundamental Theorem of Calculus, and techniques of integration like substitution. By the end of the course, learners will be able to understand and apply these concepts to solve mathematical problems. The teaching method includes theoretical explanations, examples, and problem-solving sessions. This course is intended for students or individuals interested in deepening their knowledge of calculus and improving their problem-solving skills in mathematics.
Overview
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
