![]() ![]() However, we know that the exponential function is the only function which equals its derivative.First Principles of the Differential and Integral Calculus, or the Doctrine of Fluxions (1824) First Principles of the Differential and Integral Calculus, or the Doctrine of Fluxions (1824) We could solve for \(N\) as a function of time by integrating the derivative. Where \(N\) is the population size, \(t\) is time and \(k\) is a proportionality constant. In models of exponential growth we assume that the growth rate is proportional to the population size. The inverse operation to differentiation is called antidifferentiation or, more commonly, integration. Thus we wish to know the magnitude of a quantity (body level of pollutant) when we know only the rate of change of that quantity (rate of increase by absorption and rate of decrease by excretion). However, the mathematical model may be based on the rate of absorption through the skin and rate of excretion via the urine. This operation is called integration and its field of mathematical study is called integral calculus.įor example, we may wish to know the blood level of a toxic material that is absorbed through the skin during a certain time period. We then need to use an inverse operation on the derivative to determine the desired function. In mathematical terms, we often can determine equations involving the derivatives of functions instead of the functions themselves. Frequently, the obvious relations involve rates of change of the quantities of interest, and not the quantities themselves. Most applications of calculus to ecological problems involve the determination of specific relationships between measured quantities. 16.6 Mapping the heat limit of the Desert Iguana.16.5 Mapping the cold limits of the Desert Iguana.16.4 Mapping the climate space of the Desert Iguana in North America.16.3 Getting the climate space available in Australia.14.5.3 Boundary Layers and Non-dimensional Numbers: A Bulk Approach.14.4.1 Viscosity and Laminar Shear Flows.13.5.3 Comparison of Theory with Experiment.13.5.2 Properties of the Harmonic Solution.13.5 USE OF THE HEAT CONDUCTION EQUATION.13.4.3 Heat Conduction (Diffusion) Equation.13.4.2 Heat Storage and Energy Conservation.13.4.1 Fourier’s Law of Heat Conduction.13.3 GOVERNING FACTORS IN SOIL HEAT FLOW.12.7 HEAT GAINED BY ABSORPTION OF RADIATION.12.4 HEAT TRANSFER BY CONDUCTION WITHIN THE ANIMAL.11.7.2 Sample Plots of Transpiration and Leaf Temperature.11.7.1 Calculations of Leaf Temperatures and Transpiration.11.5 INFLUENCE OF ENERGY COMPONENTS ON LEAF TEMPERATURE.11.4.2 Values of the Environmental Variables.10.4.2 Laboratory and Field Applicatons of the Operative Environmental Temperatures. ![]() 10.4.1 Mathematical Development of the Operative Environmental Temperature.10.4 THE OPERATIVE ENVIRONMENTAL TEMPERATURE.10.3.2 Thermoregulation and the Ecogeographical Rules.9.5 EXTENSIONS OF THE CLIMATE SPACE IDEA.9.4.4 Plotting the climate space of the Zebra Finch.9.4.3 Plotting the climate space of the Desert Iguana.9.4.2 Plotting climate space boundaries for a cylinder with varing solar absorptivity.9.4.1 Defining a function for computing the bounding air temperature/radiation combinations.9.4 PHYSIOLOGICAL CONTRAINTS OF THE ORGANISM.9.3 THE THERMAL ENVIRONMENT: BASIS FOR THE CLIMATE SPACE.6.7.1 General Texts and Papers on Energy Budgets.6.3.3 The First Law Generalized to Include Mass Flow.6.3 APPLICATIONS OF THE FIRST LAW OF THERMODYNAMICS.4.5.4 Gravitational and Electrostatic Potential Energy.4.4.2 Other Force “Laws”–Friction, Intermolecular Forces, Hooke’s Law.4 Foundations of Physical Theory I: Force and Energy.3.4.2 INTENSIVE AND EXTENSIVE PROPERTIES.3.4.1 THE DIMENSIONAL CONSTRAINTS ON DEFINITIONAL AND EMPIRICAL EQUATIONS.3.3.6 AUXILIARY PREFIXES OF THE METRIC SYSTEM TO INDICATE DECIMAL MULTIPLES AND SUBMULTIPLES.3.3.3 SUPPLEMENTARY MECHANICAL UNITS (cgs and English systems).2.4.2 Critical Points in Three Dimensions.1.12 SOLUTION TO THE ADDITIONAL PROBLEMS.1.6.1 Accumulation of Changes in the Function. ![]()
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