Differential Equations
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This course is a study of ordinary differential equations with applications in the physical and social sciences.
Topics include: Definitions and Terminology, Solutions, Implicit Solutions, Families of Solutions and Systems of Differential Equations.
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 differential equations class.
This course is consistently being populated with new videos.
This course is for anyone who wants to fortify their understanding of differential equations or anyone that wishes to learn differential equations can benefit from this course.
This course is consistently monitored ready to reply to any questions that may arise.
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Section 1: Introduction | |||
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Lecture 1 | 01:14 | ||
This video gives an overview of what will be covered in this course. | |||
Section 2: Definitions and Terminology | |||
Lecture 2 | 13:19 | ||
This video introduces the basic definitions and terminology of differential equations. The topics covered include classification of differential equations by type, order and linearity. | |||
Lecture 3 | 09:15 | ||
This video introduces the basic definitions and terminology of differential equations. This video goes over 4 basic examples covering how to classify ordinary differential equations by order and linearity. | |||
Lecture 4 | 10:19 | ||
This video introduces the basic definitions and terminology of differential equations. This video goes over 6 examples covering how to classify ordinary differential equations by order and linearity. |
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Lecture 5 | 10:15 | ||
This video introduces the basic definitions and terminology of differential equations. This video goes over 8 examples covering how to classify Partial Differential Equations (PDE) by order and linearity | |||
Section 3: Solutions | |||
Lecture 6 | 10:19 | ||
This video introduces the basic concepts associated with solutions of ordinary differential equations. Topics covered include: Solution to an ODE, Interval of definition, and solution curves. |
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Lecture 7 | 06:31 | ||
This video introduces the basic concepts associated with solutions of ordinary differential equations. This video goes over 3 examples illustrating how to verify solutions to differential equations. In addition this video also covers how to determine an appropriate interval of definition. | |||
Lecture 8 | 08:32 | ||
This video introduces the basic concepts associated with solutions of ordinary differential equations. This video goes over 3 slightly more challenging examples illustrating how to verify solutions to differential equations. In addition this video also covers how to determine an appropriate interval of definition. |
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Lecture 9 | 07:33 | ||
This video introduces the basic concepts associated with solutions of partial differential equations. This video goes over 3 examples illustrating how to verify solutions to partial differential equations. |
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Section 4: Implicit Solutions | |||
Lecture 10 | 09:45 | ||
This video introduces the basic concepts associated with solutions of ordinary differential equations. This video goes over implicit solutions of differential equations. The concept of a formal solution is also presented. |
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Lecture 11 | 07:45 | ||
This video introduces the basic concepts associated with solutions of ordinary differential equations. This video goes over 2 examples illustrating how to verify implicit solutions, find explicit solutions, and define appropriate intervals of definition. | |||
Lecture 12 | 08:04 | ||
This video introduces the basic concepts associated with solutions of ordinary differential equations. This video goes over 2 slightly more challenging examples illustrating how to verify implicit solutions, find explicit solutions, and define appropriate intervals of definition. |
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Section 5: Families of Solutions | |||
Lecture 13 | 10:12 | ||
This video introduces the basic concepts associated with solutions of ordinary differential equations. This video goes over families of solutions. In addition, particular solutions, general solutions, singular solutions, and piecewise-defined solutions are also presented. | |||
Lecture 14 | 08:23 | ||
This video introduces the basic concepts associated with solutions of ordinary differential equations. This video goes over 3 examples illustrating how to verify general solutions of ordinary differential equations. | |||
Lecture 15 | 06:34 | ||
This video introduces the basic concepts associated with solutions of ordinary differential equations. This video goes over 2 examples illustrating how to verify Implicit One-Parameter Family of solutions. | |||
Lecture 16 | 07:18 | ||
This video introduces the basic concepts associated with solutions of ordinary differential equations. This video goes over an example illustrating how to verify a particular solution of the one-parameter family of solutions, specifically a piecewise defined solution. | |||
Section 6: Systems of Differential Equations | |||
Lecture 17 | 08:00 | ||
This video introduces the basic concepts associated with solutions of ordinary differential equations. This video covers the basics of systems of ordinary differential equations. This video also goes over two examples illustrating how to verify solutions to systems of differential equations. |
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Section 7: Conclusion | |||
Lecture 18 | 00:52 | ||
This video gives an overview of the content that was covered in this course. |
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