Calculus Revisited is a series of videos and related resources that covers the materials normally found in a freshman-level introductory calculus course.  The series was first released in 1970 as a way for people to review the essentials of calculus.  It is equally valuable for students who are learning calculus for the first time.

Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman- and sophomore-level introductory mathematics courses. Multivariable Calculus is the second course in the series, consisting of 26 videos, 4 Study Guides, and a set of Supplementary Notes. The series was first released in 1971 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time.

This online textbook provides an overview of Calculus in clear, easy to understand language designed for the non-mathematician.

This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts.

Differential calculus in one and several dimensions. Java applets and spreadsheet assignments. Vector algebra in 3D, vector- valued functions, gradient, divergence and curl, Taylor series, numerical methods and applications. Given in the first half of the first term. However, those wishing credit for 18.013A only, must attend the entire semester. Prerequisites: a year of high school calculus or the equivalent, with a score of 4 or 5 on the AB, or the AB portion of the BC, Calculus test, or an equivalent score on a standard international exam, or a passing grade on the first half of the 18.01 Advanced Standing exam.

Calculus with Theory, covers the same material as 18.01 (Single Variable Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus.

This learning video uses a simple analog setup to explore why earthquakes are so unpredictable. The setup is simple enough that students should be able to assemble and operate it on their own with a teacher's supervision. The teaching approach used in this module is known as the 5E approach, which stands for Engagement, Exploration, Explanation, Elaboration, and Evaluation. Over the course of this lesson, the basic mechanisms that give rise to the behavior of the simple analog system are explained, and further elaboration helps the students to apply their understanding of the analog system to complex fault systems that cause earthquakes

Subject addresses the evolution of the modern capitalist economy and evaluates its current structure and performance. Various paradigms of economics are contrasted and compared (neoclassical, Marxist, socioeconomic, and neocorporate) in order to understand how modern capitalism has been shaped and how it functions in today's economy. Readings include classics in economic thought as well as contemporary analyses. Subject stresses general analytic reasoning and problem formulation rather than specific analytic techniques. May not be used for economics concentration. One economics HASS-D subject may be used as an economics elective for the economics major and minor. This course examines the implications of economic theories for social and political organization in the context of the historical evolution of industrial societies. Among the authors whose theories will be discussed are Ayn Rand, Milton Friedman, Karl Marx, Max Weber, Joseph Schumpeter, and John Kenneth Galbraith. Emphasis will be placed on class discussion of specific texts. Students will be encouraged to ground their views in concrete textual and empirical material and to consider the implications of different arguments for the understanding of personal, political, and economic events today.

This course has been designed as a seminar to give students an understanding of how scientists with medical or scientific degrees conduct research in both hospital and academic settings. There will be interactive discussions with research clinicians and scientists about the career opportunities and research challenges in the biomedical field, which an MIT student might prepare for by obtaining an MD, PhD, or combined degrees. The seminar will be held in a case presentation format, with topics chosen from the radiological sciences, including current research in magnetic resonance imaging, positron emission tomography and other nuclear imaging techniques, and advances in radiation therapy. With the lectures as background, we will also examine alternative and related options such as biomedical engineering, medical physics, and medical engineering. We'll use as examples and points of comparisons the curriculum paths available through MIT's Department of Nuclear Science and Engineering. In past years we have given very modest assignments such as readings in advance of or after a seminar, and a short term project.

Introduction to urban form and design, focusing on the physical, historical, and social form of cities. Selected cities are analyzed, drawn, and compared, to develop a working understanding of urban and architectural form. The development of map making and urban representation is discussed, and use of the computer is required. Special focus on the historical development of the selected cities, especially mid-nineteenth and mid-twentieth century periods of expansion. Readings on urban design theory in the twentieth century and a weekly discussion/seminar on them. Methods class for S.M.Arch.S. students in Architecture and Urbanism.

" TV programs such as "Law and Order" show how forensic experts are called upon to give testimony that often determines the outcome of court cases. Engineers are one class of expert who can help display evidence in a new light to solve cases. In this seminar you will be part of the problem-solving process, working through both previously solved and unsolved cases. Each week we will investigate cases, from the facts that make up each side to the potential evidence we can use as engineers to expose culprits. The cases range from disintegrating airplane engines to gas main explosions to Mafia murders. This seminar will be full of discussions about the cases and creative approaches to reaching the solutions. The approach is hands-on so you will have a chance to participate in the process, not simply study it. Some background reading and oral presentation are required."

This video will help students, particularly those not in AP-level classes, have a practical application for knowing about the major divisions between plants, particularly about the details of plant anatomy and reproduction. Students will be able to :Identify the major evolutionary innovations that separate plant divisions, and classify plants as belonging to one of those divisions based on phenotypic differences in plants. Classify plants by their pollen dispersal methods using pollen dispersal mapping, and justify the location of a _„ƒcrime scene_„Ž using map analysis. Analyze and present their analysis of banding patterns from DNA fingerprinting done using plants in a forensic context.

This video lesson aims to motivate students about chemistry and to raise their awareness about how chemistry helps in solving certain environmental problems. In this lesson, the air pollution problem created by cars and other vehicles is presented. The lesson will highlight causes of this problem, harmful products from it and possible solutions. There will also be discussion of ways to convert the pollutants produced by burning oil in vehicles into more friendly products.

The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields.

This course examines the causes of war, with a focus on practical measures to prevent and control war. Topics include causes and consequences of misperception by nations; military strategy and policy as cause of war; religion and war; U.S. foreign policy as a cause of war and peace; and the likelihood and possible nature of great wars in the future.

The historical cases covered include World War I, World War II, the Korean War, the Seven Years' War, the Arab-Israel conflict, other recent Mideast wars, and the Peloponnesian War.

Biology of cells of higher organisms: structure, function, and biosynthesis of cellular membranes and organelles; cell growth and oncogenic transformation; transport, receptors and cell signaling; the cytoskeleton, the extracellular matrix, and cell movements; chromatin structure and RNA synthesis.

The goal of this course is to teach both the fundamentals of nuclear cell biology as well as the methodological and experimental approaches upon which they are based. Lectures and class discussions will cover the background and fundamental findings in a particular area of nuclear cell biology. The assigned readings will provide concrete examples of the experimental approaches and logic used to establish these findings. Some examples of topics include genome and systems biology, transcription, and gene expression.

Subject covers all major areas of cellular and molecular neurobiology including excitable cells and membranes, ion channels and receptors, synaptic transmission, cell type determination, axon guidance and targeting, neuronal cell biology, synapse formation and plasticity. Includes lectures and exams, and involves presentation and discussion of primary literature. Focus on major concepts and recent advances in experimental neuroscience.

The endoplasmic reticulum (ER) orchestrates different cellular processes by which proteins are synthesized, correctly folded, modified and ultimately transported to their final destinations. As part of this crucial biosynthetic process, proteins that are not properly folded and consequently detrimental to normal cellular function are constantly generated. A common signature of many neurodegenerative diseases, including Alzheimer's and Parkinson's, is accumulation and deposition of misfolded proteins that arise when the ability of cells to deal with the burden of misfolded proteins is compromised. In this course, we will explore how the ER quality control machinery ensures that only properly assembled proteins exit the ER while distinguishing between nascent proteins en route to their biologically active folded state from those that are terminally misfolded.

In this course we will explore how altered metabolism drives cancer progression. Students will learn (1) how to read, discuss, and critically evaluate scientific findings in the primary research literature, (2) how scientists experimentally approach fundamental issues in biology and medicine, (3) how recent findings have challenged the traditional “textbook” understanding of metabolism and given us new insight into cancer, and (4) how a local pharmaceutical company is developing therapeutics to target cancer metabolism in an effort to revolutionize cancer therapy.