Calculus II (Integral Calculus)
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The course includes several techniques of integration, improper integrals, antiderivatives, application of the definite integral, differential equations, and approximations using Taylor polynomials and series. This course is required of engineering, physics, and mathematics majors.
This course contains a series of video tutorials that are broken up into various levels. Each video builds upon the previous one. Level I videos lay out the theoretical frame work to successfully tackle on problems covered in the next videos.
These videos can be used as a stand along course or as a supplement to your current calculus II course.
This course is consistently being populated with new videos.
This course is for anyone who wants to fortify their understanding of calculus II or anyone that wishes to learn calculus II can benefit from this course.
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Section 1: Introduction | |||
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Lecture 1 | 00:40 | ||
This video gives an overview of what this course will cover. |
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Section 2: Integration By Parts | |||
Lecture 2 | 07:30 | ||
This video goes over a second integration technique used to find indefinite integrals formed by a product of functions. This video goes over the derivation of the integration by parts formula by using the product rule as a starting point. In addition, the video goes over an example covering the application of this new integration technique. | |||
Lecture 3 | 06:55 | ||
This video goes over 3 examples, covering the proper way to use the integration by parts formula. This video includes an example covering the two forms of the integration by parts formula, an example where rewriting of the integrand is required, and a final example where an integral contains a single function. | |||
Section 3: Integration By Parts: Tabular Method | |||
Lecture 4 | 06:29 | ||
This video goes over 2 examples, covering the proper way to find integrals that require the repeated application of the integration by parts formula. In addition, the tabular method for integration by parts is also introduced. | |||
Lecture 5 | 04:16 | ||
This video goes over an example, covering the proper way to find integrals that require the repeated application of the integration by parts formula specifically an integral that generates a constant multiple of the original integral. In addition, this integral will also be found by using the tabular method for integration by parts. | |||
Lecture 6 | 06:32 | ||
This video goes over three examples, covering the proper way to find definite integrals that require the application of the integration by parts formula. An example covering the tabular method is also presented. | |||
Section 4: Multiple Integration Techniques | |||
Lecture 7 | 07:04 | ||
This video goes over two examples, covering the proper way to find definite integrals that require the use of multiple integration techniques. Specifically, integration by parts and u-substitution. | |||
Section 5: Trigonometric Integrals | |||
Lecture 8 | 10:31 | ||
This video is an introduction to solving trigonometric integrals that contain combinations of trigonometric functions. Specifically, those that contain powers of sine and cosine. This video covers 4 basic examples illustrating the case when the power of cosine is odd. | |||
Lecture 9 | 10:53 | ||
This video is an introduction to solving trigonometric integrals that contain combinations of trigonometric functions. Specifically, those that contain powers of sine and cosine. This video covers 4 basic examples illustrating the case when the power of sine is odd. | |||
Lecture 10 | 06:26 | ||
This video is an introduction to solving trigonometric integrals that contain combinations of trigonometric functions. Specifically, those that contain powers of sine and cosine. This video covers 1 basic example illustrating the case when the power of sine and cosine are odd. | |||
Section 6: Even Powers | |||
Lecture 11 | 09:48 | ||
This video is an introduction to solving trigonometric integrals that contain combinations of trigonometric functions. Specifically, those that contain powers of sine and cosine. This video covers 2 basic example illustrating the case when the power of sine and cosine are even. | |||
Lecture 12 | 09:30 | ||
This video continues illustrating methods in solving trigonometric integrals that contain combinations of trigonometric functions. Specifically, those that contain powers of sine and cosine. This video covers 2 challenging examples illustrating the case when the power of sine and cosine are even. | |||
Section 7: Distinct Arguments | |||
Lecture 13 | 09:17 | ||
This video continues illustrating methods for solving trigonometric integrals that contain combinations of trigonometric functions. Specifically, those that contain products of sine and cosine with distinct arguments (angles). This video covers 3 examples illustrating the use of the product to sum identities for sine and cosine. | |||
Lecture 14 | 09:48 | ||
This video concludes the methods for solving trigonometric integrals that contain combinations of sine and cosine. This video covers 4 challenging examples that require the use of different trigonometric identities, multiplying by the conjugate, and factoring. | |||
Section 8: Conclusion | |||
Lecture 15 | 00:34 | ||
This video gives an overview of what was taught in this course. |
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