A Brief Summary of Calculus
Chapter 1 is a brief development of one-variable calculus. The opening section presents the concept of the parameter, which is essential in modeling and helpful in calculus. Differential calculus occupies Sections 1.2–1.6, with one section each on the derivative concept, derivative computation, local behavior and linear approximation, optimization, and related rates. The final three sections introduce the definite integral as the accumulation of change, present the properties of definite integrals, and calculate definite integrals using the fundamental theorem of calculus and the substitution technique. Examples with biological relevance include atmospheric carbon dioxide, organism growth, optimal foraging, the Deepwater Horizon oil spill, and population growth and demographics. The problem sets contain some modeling problems, including several on population demographics and two that explore explanations of optimal fetching behavior observed in dogs.
KeywordsTangent Line Fundamental Theorem Chain Rule Local Behavior Local Extremum
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