Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn’t a prereq) so don’t confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We’ve also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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The pendulum rotates clockwise and counterclockwise in the most unexpected and surprising fashion, changing directions or suddenly increasing speed just when you think you know what they’re going to do next. (A quote from Harvard Natural Sciences Lecture Demonstrations). This is “a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to…

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! ðŸ™‚ https://www.patreon.com/patrickjmt !! Evaluating a Line Integral Along a Straight Line Segment. In this video, I evaluate a line integral along a straight line segment by using a parametric representation of the curve (using a vector representation…

This video by Fort Bend Tutoring shows the process of graphing quadratic functions and equations. Emphasis is placed on finding the vertex and using an xy-chart. Tips on using transformations are also mentioned. Seven (7) examples of graphing quadratic functions are shown that include standard form and vertex form. This math concept, quadratic functions and…