Derivatives
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This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space.
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Topics covered in the first two or three semesters of college calculus. Everything from limits to derivatives to integrals to vector calculus. Should understand the topics in the pre-calculus playlist first (the limit videos are in both playlists).
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Financial institutions are a pillar of civilized society, supporting people in their productive ventures and managing the economic risks they take on. The workings of these institutions are important to comprehend if we are to predict their actions today and their evolution in the coming information age. The course strives to offer understanding of the theory of finance and its relation to the history, strengths and imperfections of such...more
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Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes.
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Professor Diamond continues her discussion of the nervous system beginning with a discussion of myelin-forming oligodendrocytes and Schwann cells, saltatory conduction from the nodes of ranvier, and the similarity of the function of microglia to monocytes. She moves on to describe the development of the neural tube by drawing a cross-section of the neural tube and depicting the changes it undergoes, forming the ventricles of the brain,...more
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Half a century before direct experimental observation became possible, most structures of organic molecules were assigned by inspired guessing based on plausibility. But Wilhelm Körner developed a strictly logical system for proving the structure of benzene and its derivatives based on isomer counting and chemical transformation. His proof that the six hydrogen positions in benzene are equivalent is the outstanding example of this...more
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Carboxylic Acid Derivatives - Amides, Anhydrides, Esters and Acyl Chlorides.
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Intuition on what happens to the slope/derivative and second derivatives at local maxima and minima.
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Calculus finds the relationship between the distance traveled and the speed — easy for constant speed, not so easy for changing speed. Professor Strang is finding the rate of change, the slope of a curve, and the derivative of a function.
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Calculus-Derivative: Understanding that the derivative is just the slope of a curve at a point (or the slope of the tangent line).
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Professor Diamond continues her discussion of the nervous system, finishing her discussion of the derivatives of the neural tube. She begins by discussing the lamina terminalis and the four ventricles, relating each to the source of their derivation and the areas of the brain in which they are found. Next, she continues her discussion of diencephalon from the last lecture and describes the roles of the thalamus and hypothalamus. After...more
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