Master the calculus of derivatives, integrals, coordinate systems, and infinite series.
In this three-part series you will learn the mathematical notation, physical meaning, and geometric interpretation of a variety of calculus concepts. Along with the fundamental computational skills required to solve these problems, you will also gain insight into real-world applications of these mathematical ideas.

Part 1: Differentiation
Part 2: Integration
Part 3: Coordinate Systems & Infinite Series

This series of courses is part of the Open Learning Library, which is free to use. You have the option to sign up and enroll in the courses if you want to track your progress, or you can view and use all the materials without enrolling.

First published in 1991 by Wellesley-Cambridge Press, this updated 3rd edition of the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor’s Manual and a student Study Guide.

Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman- and sophomore-level introductory mathematics courses. Complex Variables, Differential Equations, and Linear Algebra is the third course in the series, consisting of 20 Videos, 3 Study Guides, and a set of Supplementary Notes. Students should have mastered the first two courses in the series (Single Variable Calculus and Multivariable Calculus) before taking this course.
The series was first released in 1972, but equally valuable today for students who are learning these topics for the first time.
About the Instructor
Herb Gross has taught math as senior lecturer at MIT and was the founding math department chair at Bunker Hill Community College. He is the developer of the Mathematics As A Second Language website, providing arithmetic and algebra materials to elementary and middle school teachers.
Acknowledgements
Funding for this resource was provided by the Gabriella and Paul Rosenbaum Foundation.
Other Resources by Herb Gross
Calculus Revisited: Single Variable Calculus 
Calculus Revisited: Multivariable Calculus

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.
About the Instructor
Herb Gross has taught math as senior lecturer at MIT and was the founding math department chair at Bunker Hill Community College. He is the developer of the Mathematics As A Second Language website, providing arithmetic and algebra materials to elementary and middle school teachers.
Acknowledgements
Funding for this resource was provided by the Gabriella and Paul Rosenbaum Foundation.
Other Resources by Herb Gross
Calculus Revisited: Single Variable Calculus
Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra

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.
About the Instructor
Herb Gross has taught math as senior lecturer at MIT and was the founding math department chair at Bunker Hill Community College. He is the developer of the Mathematics As A Second Language website, providing arithmetic and algebra materials to elementary and middle school teachers.
Acknowledgements
Funding for this resource was provided by the Gabriella and Paul Rosenbaum Foundation.
Other Resources by Herb Gross
Calculus Revisited: Multivariable Calculus
Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra

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

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.
Acknowledgement
Prof. McKernan would like to acknowledge the contributions of Lars Hesselholt to the development of this course.

This is an undergraduate course on differential calculus in one and several dimensions. It is intended as a one and a half term course in calculus for students who have studied calculus in high school. The format allows it to be entirely self contained, so that it is possible to follow it without any background in calculus.

18.014, 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 course 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. The course stresses general analytic reasoning and problem formulation rather than specific analytic techniques. Readings include classics in economic thought as well as contemporary analyses.

The decades leading up to the Atlantic revolutions of the late eighteenth century were formative moments in the rise of capitalism. The novel instruments of credit, debt, and investment fashioned during this period proved to be enduring sources of financial innovation, but they also generated a great deal of political conflict, particularly during the revolutionary era itself.  This seminar examines the debates surrounding large-scale financial and trading corporations and considers the eighteenth century as a period of recurring financial crisis in which corporate power came into sustained and direct contact with emerging republican norms. The seminar ends with a look at the relationship between slavery and the rise of “modern” or “industrial” capitalism in the nineteenth century, as well as some of the critiques of capitalism that emerged out of that experience.

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.

Carrier systems involve the design, operation and management of transportation networks, assets, personnel, freight and passengers. In this course, we will present models and tools for analyzing, optimizing, planning, managing and controlling carrier systems.

This course serves as an 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. A special focus is placed on the historical development of the selected cities, especially mid-nineteenth and mid-twentieth century periods of expansion. Readings focus on urban design theory in the twentieth century and will be discussed during a weekly seminar on them. This is a 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.

The MIT Case Studies in Social and Ethical Responsibilities of Computing (SERC) aims to advance new efforts within and beyond MIT’s Stephen A. Schwarzman College of Computing. The specially commissioned and peer-reviewed cases are brief and intended to be effective for undergraduate instruction across a range of classes and fields of study. The series editors expect the cases will also be of interest for computing professionals, policy specialists, and general readers. All cases will be made freely available via open-access publishing, with author retained copyright, through Creative Commons licensing.
The Series Editors interpret “social and ethical responsibilities of computing” broadly. Some cases focus closely on particular technologies, others on trends across technological platforms. Still others examine social, historical, philosophical, legal, and cultural facets that are essential for thinking critically about present-day efforts in computing and data sciences.

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.

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.

Mechanical forces play a decisive role during development of tissues and organs, during remodeling following injury as well as in normal function. A stress field influences cell function primarily through deformation of the extracellular matrix to which cells are attached. Deformed cells express different biosynthetic activity relative to undeformed cells. The unit cell process paradigm combined with topics in connective tissue mechanics form the basis for discussions of several topics from cell biology, physiology, and medicine.