Courses tagged with "Taking derivatives" (66)

Botany is the study of plants.  Because species in the plant kingdom have characteristics that make them distinct from any other form of life, they are particularly interesting subjects for the study of evolution and physiology.  For example, whereas most organisms are dependent on other organisms for energy, plants can capture energy directly from photons of light and convert it into a usable form through the process of photosynthesis.  For this reason, plants are referred to as the “producers” in a habitat.  Unlike the cells of other organisms, plant cells have rigid cell walls constructed from the inside out (rather than the outside in) during mitosis and cytokinesis.  Plants also have a variety of unique reproductive and dispersal mechanisms that allow them to quickly adapt to, occupy, and invade far-flung areas, despite their general immobility. In this course, you will learn the basics of plant biology.  We will begin with plant anatomy, learning the names and functions of all of the parts o…

Even in ancient times, scholars believed that diseases could be spread by organisms too small to be seen by the naked eye. Before we discovered that bacteria cells were the real culprits, many attributed disease to other sources. Now that scientists have definitively identified the microscopic causes of various infectious diseases, microbiology, or the study of microscopic-sized organisms, has become an increasingly important field in biology and in the larger biomedical community. Most microbes are harmless. Some of them are essential for life on Earth, e.g. through their ability to fix nitrogen. Biotechnology, which is truly the industry of our times, takes advantage of microbes for the production of a variety of complex substances, and it also mass-produces natural and engineered microbes for human use. This course will cover a range of diverse areas of microbiology, including virology, bacteriology, and applied microbiology. This course will focus on the medical aspects of microbiology, as medical res…

Marine Biology is the study of ocean life.  As you might expect, life in salt water is vastly different from life in a terrestrial or freshwater environment due to factors like salinity, water circulation, and atmospheric pressure.  How, for example, can organisms living in salt water avoid dehydration?  How do organisms living in the depths of the ocean handle the immense pressure?  How do the environmental factors in marine communities affect biodiversity?  How do some animals manage to alternate between the demands of terrestrial life and the demands of marine life?  In this course, you will learn the answers to these questions and more.  This course will touch on a number of different subfields of biological study (including biochemistry, physiology, zoology, botany, and ecology) within the context of the ocean environment. You will start by learning about the ocean itself and its physical properties, as these properties influence the abundance, distribution, diversity, physiology, and behavior o…

Zoology is the scientific study of diversity of animal life, classification, physiology, behavior, and evolution. Unicellular organisms have evolved into complex multicellular forms. Organisms, both unicellular and multicellular, in various complex shapes and sizes are found in almost every habitat and environment. The field of zoology includes many subfields of biology as well as a vast diversity of unicellular and multicellular organisms. Animals first appeared in the fossil record an estimated 600 million years ago as multicellular protozoa. Over the next 70 million years, they radiated into an incredible number of different invertebrate phyla (which represent the majority of animal groups and species), and in the next 150 million years, vertebrate and invertebrate species began to colonize the land. Though the history of animals is extensive and the fossil record at times is conflicted and vague, understanding the historical connections between animals is important in order to understand modern-day rela…

Developmental biology asks questions about how organisms come into being, how life forms, and how complex structures develop and are differentiated.  These fundamental questions have been the subject of research for centuries; accordingly, this course you will teach you not only about the beginnings of organisms, but about the beginnings of developmental biology as a science.  Currently, developmental biologists use a range of tools and research focifrom molecular techniques to surgical manipulations to chemical and environmental studiesto answer these questions.  Their approaches are multi-faceted because developmental biology itself addresses topics of importance to a wide range of fields, from molecular biology to neuroscience to evolutionary biology. In this course, you will learn about the field of developmental biology from its origins to the present day.  We will take a look at historical experiments as well as modern techniques and the mechanisms of development.  You will follow a variety of me…

Molecular biology studies the molecular mechanisms of life, particularly those responsible for genes and their expression.  In the center of molecular biology are the nucleic acids, DNA and RNA, and how they contribute to the synthesis of proteins. After a historical introduction (Unit 1), this course describes the basic types of DNA and RNA structure and the molecular interactions that shape them (Unit 2).  Unit 3 describes how DNA is packaged within the cellular nucleus as chromosomes; in eukaryotes the DNA coils around histones to form nucleosomes that comprise the chromatin of the chromosomes.  The next three units describe the core processes of molecular biology: replication of DNA (Unit 4), transcription of DNA into messenger RNA (Unit 5), and translation of messenger RNA into a protein (Unit 6).  These are followed by modifications of these basic processes: regulation of gene expression (Unit 7), DNA mutation and repair (Unit 8), and DNA recombination and transposition (Unit 9). The course conclu…

One of the best ways to understand the present is to understand the past. Evolutionary Biology is the study of the changes in life forms over time - changes that have occurred over millions of years as well as those that have occurred over just a few decades. In this course, we will look at the various mechanisms of evolution, how these mechanisms work, and how change is measured. The concepts you learn in this course will serve as a foundation for studying fossil records and current classification schemes in biology. We will begin the course by reviewing the evolutionary concepts of selection and speciation. We will then learn to measure evolutionary change through comparisons with the Hardy-Weinberg Equilibrium, to understand the process of change through Game Theory, and to interpret and classify changes by creating phylogenies. The course will wrap up with a look at the history of life according to the fossil record and a discussion of the broad range of life forms as they are currently classified. At the…

Ecology is the study of interactions between organisms and between organisms and their environments.  Population ecology is the subfield of ecology that identifies those ecological factorsin the community or in the ecosystemthat regulate a population’s size. Ecosystems and communities involve complex interactions that have evolved over long periods of time.  The species that are present and the interactions we see between them are the result of evolution under the unique environmental pressures that exist in a given environment.  These interactions may be delicately intertwined, such that the loss of a single species from a community could mean the collapse of the entire community in a domino effect.  Thus, biologists are concerned with the preservation of biodiversity in ecosystemsretaining as many different species in the ecosystem as possible so the intricate relationships among species are preserved. In recent years, we have seen a decrease in the biodiversity of ecosystems.  Human activities a…

Biochemistry is the study of the chemical processes and compounds, such as cellular makeup, that bring about life in organisms.  It is a combination of multiple science fields; you can think of it as general and cell biology coupled with organic and general chemistry.  Although living organisms are very complex, from a molecular view, the material that constitutes “life” can be broken down into remarkably simple molecules, much like the breakdown of our English language to the English alphabet.  Although there exists thousands upon thousands of molecules, they all breakdown into four core components: nucleic acids, amino acids, lipids, and carbohydrates.  As we can make hundreds of thousands of words from just 26 letters, we can make thousands of different biomolecules from those 4 components.  For example, the human genome, containing the necessary information to create a human being, is really just one very long strand of 4 different nucleotides. This course is structured around that approach, so…

The purpose of this course is to explore the subject of human disease, placing special emphasis on the cause of disease at the tissue level.  We will pay close attention to the underlying mechanisms that initiate and perpetuate the disease state.  Much can be learned about the causes of disease at the molecular and cellular level; we will accordingly spend quite a bit of time examining molecules, cells, and tissues and determining how the disruption of their normal functioning by various known and unknown causes can lead to disease. We will begin this course with a basic review of molecules, cells, and tissues in the human body.  We will then discuss the body’s first line of defense, the inflammatory reaction, and the immune system. Finally, we will survey the body’s organ systems.  We will approach each of the systems by examining the ways in which a prototype disease impacts its functioning.  (These “prototypes” will be diseases that impact a large number of patients around the world.)  We…

Biotechnology is the application of biology and biological concepts to science and engineering.  It is the crossroad of the biological sciences with other major disciplines of science, from organic chemistry to mechanical engineering.  The earliest applications of biotechnology involve people of ancient civilizations using organisms to create bread and wine.  The discovery of the Penicillium mold to combat infection is another famous example, as its production involved a specially designed fermentation process using microorganisms.  Nowadays, scientists use almost all aspects of biology in their applications, from DNA to protein to cellular organelles.  Living organisms, especially microorganisms, are thought of as biochemical machinery, able to be edited and changed to create new purposes.  We could program them to create insulin for diabetes patients or to produce fuel for our cars.  Biotechnology is nearly limitless in its applications. As biotechnology is a very diverse topic, this course will in…

Cancer has existed among humans since humans themselves began and has been a subject of urgent interest from very early in our history.  What we call “cancer” consists of a number of different diseases with one fundamental similarity: they are all initiated by the unchecked proliferation and growth of cells in which the pathways and systems that normally control cell division and mortality are absent.  Cancer-cell abnormalities are often due to mutations of the genes that control the cell cycle and cell growth.  To understand cancer cells, then, one must first understand the processes that regulate normal cell cycles. This course will cover the origins of cancer and the genetic and cellular basis for cancer.  It will examine the factors that have been implicated in triggering cancers; the intercellular interactions involved in cancer proliferation; current treatments for cancer and how these are designed; and future research and treatment directions for cancer therapy.

The advent of computers transformed science.  Large, complicated datasets that once took researchers years to manually analyze could suddenly be analyzed within a week using computer software.  Nowadays, scientists can use computers to produce several hypotheses as to how a particular phenomenon works, create computer models using the parameters of each hypothesis, input data, and see which hypothetical model produces an output that most closely mirrors reality. Computational biology refers to the use of computers to automate data analysis or model hypotheses in the field of biology.  With computational biology, researchers apply mathematics to biological phenomena, use computer programming and algorithms to artificially create or model the phenomena, and draw from statistics in order to interpret the findings.  In this course, you will learn the basic principles and procedures of computational biology.  You will also learn various ways in which you can apply computational biology to molecular and cell…

In this course, you will study microscopic anatomy. The study of the structure of a cell, tissue, organ, or related feature is known as anatomy. Gross anatomy (or macroscopic anatomy) involves examining anatomical structures that can be seen with the naked eye, whereas microscopic anatomy is the examination of minute anatomical structures that cannot be observed without the help of visual enhancement, such as a microscope. The terms microscopic anatomy and histology (the study of microscopic structure of animal and plant tissue) are used interchangeably. Many times it will be necessary to survey gross anatomy so that when you focus in on the microscopic anatomy you will have a geographical idea of the location within the body. This course makes use of microscope slides of anatomical structures to aid in the discussions of anatomy. Unit 1 begins with an overview of basic cell structure. The study of cells is known as cytology. Cells contain numerous structures that can only be seen with the aid of specialize…

Immunology is the study of our immune system, a highly sophisticated system that defends us against all disease-causing invaders by identifying and neutralizing such threats. Even though we might get sick every now and then, the immune system does an incredible job of warding off infection given how many infectious agents (thousands!) we come into contact with every day. This becomes most apparent when a healthy individual compares himself or herself to an individual with little or no immune response who cannot survive in a normal environment and must rely on specialized rooms much cleaner than even a surgery room. Before the discovery of immunity, we used to associate sickness and disease with various superstitions and beliefs. Only with the discovery of bacteria, viruses, and our own cells did scientists slowly piece together the modern theory of our immune system. Our overall system can be broken down into two sub-systems, each with its own unique cells, molecules, and functions. Our cells are in turn capa…

Physics 101 is the first course in the Introduction to Physics sequence. In general, the quest of physics is to develop descriptions of the natural world that correspond  closely to actual observations.  Given this definition, the story behind everything in the universe is  one of physics.  In practice,  the field of physics is more often limited to the discovery and refinement of the basic laws that underlie the behavior of matter and energy.  While biology is founded upon physics, in practice, the study of biology generally assumes that the present understanding of physical laws is accurate.  Chemistry is more closely dependent on physics and   assumes that physical laws provide accurate predictions.  Engineering, for the most part, is applied physics. In this course, we will study physics from the ground up, learning the basic principles of physical laws, their application to the behavior of objects, and the use of the scientific method in driving advances in this knowledge.  This first course o…

The physics of the Universe appears to be dominated by the effects of four fundamental forces: gravity, electromagnetism, and weak and strong nuclear forces.  These control how matter, energy, space, and time interact to produce our physical world.  All other forces, such as the force you exert in standing up, are ultimately derived from these fundamental forces. We have direct daily experience with two of these forces: gravity and electromagnetism.  Consider, for example, the everyday sight of a person sitting on a chair.  The force holding the person on the chair is gravitational, while that gravitational force is balanced by material forces that “push up” to keep the individual in place, and these forces are the direct result of electromagnetic forces on the nanoscale.  On a larger stage, gravity holds the celestial bodies in their orbits, while we see the Universe by the electromagnetic radiation (light, for example) with which it is filled.  The electromagnetic force also makes possible the a…

This course is designed to introduce you to the study of Calculus.  You will learn concrete applications of how calculus is used and, more importantly, why it works.  Calculus is not a new discipline; it has been around since the days of Archimedes.  However, Isaac Newton and Gottfried Leibniz, two 17th-century European mathematicians concurrently working on the same intellectual discovery hundreds of miles apart, were responsible for developing the field as we know it today.  This brings us to our first question, what is today's Calculus?  In its simplest terms, calculus is the study of functions, rates of change, and continuity.  While you may have cultivated a basic understanding of functions in previous math courses, in this course you will come to a more advanced understanding of their complexity, learning to take a closer look at their behaviors and nuances. In this course, we will address three major topics: limits, derivatives, and integrals, as well as study their respective foundations and a…

This course is the second installment of Single-Variable Calculus.  In Part I (MA101) [1], we studied limits, derivatives, and basic integrals as a means to understand the behavior of functions.  In this course (Part II), we will extend our differentiation and integration abilities and apply the techniques we have learned. Additional integration techniques, in particular, are a major part of the course.  In Part I, we learned how to integrate by various formulas and by reversing the chain rule through the technique of substitution.  In Part II, we will learn some clever uses of substitution, how to reverse the product rule for differentiation through a technique called integration by parts, and how to rewrite trigonometric and rational integrands that look impossible into simpler forms.  Series, while a major topic in their own right, also serve to extend our integration reach: they culminate in an application that lets you integrate almost any function you’d like. Integration allows us to calculat…

This chemistry survey is designed to introduce students to the world of chemistry.  The principles of chemistry were first identified, studied, and applied by ancient Egyptians in order to extract metal from ores, make alcoholic beverages, glaze pottery, turn fat into soap, and much more.  What began as a quest to build better weapons or create potions capable of ensuring everlasting life has since become the foundation of modern science.  Take a look around you: chemistry makes up almost everything you touch, see, and feel, from the shampoo you used this morning to the plastic container that holds your lunch.  In this course, we will study chemistry from the ground up, learning the basics of the atom and its behavior.  We will use this knowledge to understand the chemical properties of matter and the changes and reactions that take place in all types of matter.