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Calculus: The Big Picture

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About this Course

About the Course

In this course, Professor Paul Allen (Lewis & Clark College) explains the main ideas behind calculus, with the hope that we can keep this big picture in mind when learning calculus computation techniques. In the first mini-lecture, we discuss the limitations of the equation, distance = rate × time, and see how calculus provides a resolution to this limitation using a concept called linear approximation. In the second mini-lecture, we discuss linear approximation and cumulative effect using an example of going on a 2-hour walk. We see how calculating the cumulative effect becomes more and more accurate when using smaller and smaller intervals, and we assign mathematical notation to this concept (the definite integral). In the third mini-lecture, we continue with our example of going on a 2-hour walk to further discuss linear approximation and rates of change as the motivation behind the derivative. In the fourth mini-lecture, we tie together the concepts we’ve been learning in a discussion on the Fundamental Theorem of Calculus.

About the Lecturer

Paul T. Allen is an Associate Professor of Mathematics at Lewis & Clark College in Portland, OR. His current research interests involve studying problems in geometric analysis by analysing associated partial differential equations, many of which are related to problems in mathematical relativity.