Cucurbitaceae is a family of plants first cultivated in Mesoamerica, although several species are native to North America. The family includes many edible species, such as squash and pumpkin, as well as inedible gourds. In order to grow and develop into mature, fruit-bearing plants, many requirements must be met, and events must be coordinated. Seeds must germinate under the right conditions in the soil; therefore, temperature, moisture, and soil quality are important factors that play a role in germination and seedling development. Soil quality and climate are significant to plant distribution and growth. The young seedling will eventually grow into a mature plant, and the roots will absorb nutrients and water from the soil. At the same time, the aboveground parts of the plant will absorb carbon dioxide from the atmosphere and use energy from sunlight to produce organic compounds through photosynthesis. This module will explore the complex dynamics between plants and soils, and the adaptations that plants have evolved to make better use of nutritional resources.

The arctic fox is an example of a complex animal that has adapted to its environment and illustrates the relationships between an animal’s form and function. The structures of animals consist of primary tissues that make up more complex organs and organ systems. Homeostasis allows an animal to maintain a balance between its internal and external environments.  This chapter will explore theses ideas as well as many more.

Most animals are complex multicellular organisms that require a mechanism for transporting nutrients throughout their bodies and removing waste products. The circulatory system has evolved over time from simple diffusion through cells in the early evolution of animals to a complex network of blood vessels that reach all parts of the human body. This extensive network supplies the cells, tissues, and organs with oxygen and nutrients, and removes carbon dioxide and waste, which are byproducts of respiration.

An animal’s endocrine system controls body processes through the production, secretion, and regulation of hormones, which serve as chemical “messengers” functioning in cellular and organ activity and, ultimately, maintaining the body’s homeostasis. The endocrine system plays a role in growth, metabolism, and sexual development.

People did not understand the mechanisms of inheritance, or genetics, at the time Charles Darwin and Alfred Russel Wallace were developing their idea of natural selection. Scholars rediscovered Mendel’s work in the early twentieth century, and over the next few decades scientists integrated genetics and evolution in what became known as the modern synthesis—the coherent understanding of the relationship between natural selection and genetics that took shape by the 1940s. Natural selection can affect a population’s genetic makeup, and, in turn, this can result in the gradual evolution of populations. In the early twentieth century, biologists in the area of population genetics began to study how selective forces change a population through changes in allele and genotypic frequencies.  Adaptive evolution is the process by which natural selection increases the frequency of beneficial alleles in the population, while decreasing the frequency of deleterious alleles.

The environment consists of numerous pathogens, usually microorganisms, that cause disease in their hosts. Components of the immune system constantly search the body for signs of these pathogens. Mammalian immune systems evolved for protection from such pathogens. These systems are composed of an extremely diverse array of specialized cells and soluble molecules that coordinate a rapid and flexible defense system.

The muscular and skeletal systems provide support to the body and allow for a wide range of movement. The bones of the skeletal system protect the body’s internal organs and support the weight of the body. The muscles of the muscular system contract and pull on the bones, allowing for movements as diverse as standing, walking, running, and grasping items.

A nervous system is an organism’s control center. It processes sensory information from outside and inside the body and controls all behaviors, from fundamental to complex. Although nervous systems throughout the animal kingdom vary in structure and complexity, each functions to maintain homeostasis.

After completing this section, students should be able to do the following.Compute average velocity.Approximate instantaneous velocity.Compare average and instantaneous velocity.Compute instantaneous velocity.

After completing this section, students should be able to do the following.Define an antiderivative.Compute basic antiderivatives.Compare and contrast finding derivatives and finding antiderivatives.Define initial value problems.Solve basic initial value problems.Use antiderivatives to solve simple word problems.Discuss the meaning of antiderivatives of the velocity and acceleration.

After completing this section, students should be able to do the following.Interpert the product of rate and time as area.Approximate position from velocity.Recognize Riemann sums.

After completing this section, students should be able to do the following.Given a velocity function, calculate displacement and distance traveled.Given a velocity function, find the position function.Given an acceleration function, find the velocity function.Understand the difference between displacement and distance traveled.Understand the relationship between position, velocity and acceleration.Calculate the change in the amount.Compute the average value of the function on an interval.Understand that the average value of the function on an interval is attained by the function on that interval.

After completing this section, students should be able to do the following.Identify word problems as related rates problems.Translate word problems into mathematical equations.Solve related rates word problems.

After completing this section, students should be able to do the following.Express the sum of n terms using sigma notation.Apply the properties of sums when working with sums in sigma notation.Understand the relationship between area under a curve and sums of areas of rectangles.Approximate area of the region under a curve.Compute left, right, and midpoint Riemann sums with 10 or fewer rectangles.Understand how Riemann sums with n rectangles are computed and how the exact value of the area is obtained by taking the limit as n→∞n→∞ .

After completing this section, students should be able to do the following.Recognize a composition of functions.Take derivatives of compositions of functions using the chain rule.Take derivatives that require the use of multiple rules of differentiation.Use the chain rule to calculate derivatives from a table of values.Understand rate of change when quantities are dependent upon each other.Use order of operations in situations requiring multiple rules of differentiation.Apply chain rule to relate quantities expressed with different units.Compute derivatives of trigonometric functions.Use multiple rules of differentiation to calculate derivatives from a table of values.

After completing this section, students should be able to do the following.Find the intervals where a function is increasing or decreasing.Find the intervals where a function is concave up or down.Determine how the graph of a function looks without using a calculator.

After completing this section, students should be able to do the following.Understand what information the derivative gives concerning when a function is increasing or decreasing.Understand what information the second derivative gives concerning concavity of the graph of a function.Interpret limits as giving information about functions.Determine how the graph of a function looks based on an analytic description of the function.

After completing this section, students should be able to do the following.Identify where a function is, and is not, continuous.Understand the connection between continuity of a function and the value of a limit.Make a piecewise function continuous.State the Intermediate Value Theorem including hypotheses.Determine if the Intermediate Value Theorem applies.Sketch pictures indicating why the Intermediate Value Theorem is true, and why all hypotheses are necessary.Explain why certain points exist using the Intermediate Value Theorem.

After completing this section, students should be able to do the following.Use integral notation for both antiderivatives and definite integrals.Compute definite integrals using geometry.Compute definite integrals using the properties of integrals.Justify the properties of definite integrals using algebra or geometry.Understand how Riemann sums are used to find exact area.Define net area.Approximate net area.Split the area under a curve into several pieces to aid with calculations.Use symmetry to calculate definite integrals.Explain geometrically why symmetry of a function simplifies calculation of some definite integrals.