Sage university papers series. Quantitative applications in the social sciences ;
no. 07-110
Includes bibliographical references (page 81).
1. Mathematical functions -- Graphs of functions -- Continuity -- Calculus -- Differentiation and integration -- Duality -- 2. Differentiation -- Definition of the derivative -- Simple examples -- The derivative of a sum of two functions -- Other functions -- Derivatives of a product and a quotient of two functions -- The chain rule -- Different notations -- Higher derivatives -- List of derivatives -- 3. Integration -- The definite integral -- Area and slope -- Adding small rectangles -- The fundamental theorem of calculus -- The integral as a function of a limit -- Specific integrals -- Integration methods -- List of integrals -- 4. Applications -- Maximum and minimum -- Integration -- Distance, speed, and acceleration -- Applications in statistics -- Applications in the social sciences.
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This overview of the central ideas of calculus provides many examples of how calculus is used to translate many real world phenomena into mathematical functions.