Sustainability and Calculus
Sustainability and Calculus
Introduction and Preview Calculus is all about change. Calculus provides the mathematical tools to examine important questions about dynamic behavior; e.g. how fast is the world population increasing? If we continuously release a pollutant into a lake at a known rate, what's the total amount of pollutant that will be dumped into the water in the next five years? How long will the nonrenewable supplies of coal and oil last if we maintain the current per capita use but population continues to grow? How long will supplies last if industrialization and a "rising standard of living" push per capita usage ever higher? If we disturb the natural population dynamics of a salmon species by fishing, how should we regulate our removal of fish to provide a maximal sustainable yield in the future? Although we will study many different applications of calculus in this introductory course, we will place a particular emphasis on the problem of sustainability.
Sustainability means meeting the needs of the present without compromising the ability of future generations to meet their own needs.
Our definition of sustainability comes from the 1987 publication Our Common Future by the United Nations World Commission on Environment and Development (also known as the Brundtland commission after its chair, Norwegian diplomat Gro Harlem Brundtland) We will highlight two different approaches to using calculus to investigate sustainability questions. Here we will briefly describe each approach and list some types of questions Calculus will help us answer.
Approach I: Start with Data Calculus works best if we have a specific formula in functional form for a particular relationship. Once we have a formula, we can compute rates of change or measures of accumulation using, respectively, derivatives and integrals, the two basic tools of calculus. What we often have in the real world, however, is data, not
Introduction and Preview Calculus is all about change. Calculus provides the mathematical tools to examine important questions about dynamic behavior; e.g. how fast is the world population increasing? If we continuously release a pollutant into a lake at a known rate, what's the total amount of pollutant that will be dumped into the water in the next five years? How long will the nonrenewable supplies of coal and oil last if we maintain the current per capita use but population continues to grow? How long will supplies last if industrialization and a "rising standard of living" push per capita usage ever higher? If we disturb the natural population dynamics of a salmon species by fishing, how should we regulate our removal of fish to provide a maximal sustainable yield in the future? Although we will study many different applications of calculus in this introductory course, we will place a particular emphasis on the problem of sustainability.
Sustainability means meeting the needs of the present without compromising the ability of future generations to meet their own needs.
Our definition of sustainability comes from the 1987 publication Our Common Future by the United Nations World Commission on Environment and Development (also known as the Brundtland commission after its chair, Norwegian diplomat Gro Harlem Brundtland) We will highlight two different approaches to using calculus to investigate sustainability questions. Here we will briefly describe each approach and list some types of questions Calculus will help us answer.
Approach I: Start with Data Calculus works best if we have a specific formula in functional form for a particular relationship. Once we have a formula, we can compute rates of change or measures of accumulation using, respectively, derivatives and integrals, the two basic tools of calculus. What we often have in the real world, however, is data, not