This Project has been completed as part of a standard Calculus 3 synchronous online course during Spring 2021 Semester at MassBay Community College, Wellesley Hills, MA.
This textbook covers calculus of a single variable, suitable for a year-long (or two-semester) course. Chapters 1-5 cover Calculus I, while Chapters 6-9 cover Calculus II. The book is designed for students who have completed courses in high-school algebra, geometry, and trigonometry. Though designed for college students, it could also be used in high schools. The traditional topics are covered, but the old idea of an infinitesimal is resurrected, owing to its usefulness (especially in the sciences).
This subject provides an introduction to fluid mechanics. Students are introduced to and become familiar with all relevant physical properties and fundamental laws governing the behavior of fluids and learn how to solve a variety of problems of interest to civil and environmental engineers. While there is a chance to put skills from calculus and differential equations to use in this subject, the emphasis is on physical understanding of why a fluid behaves the way it does. The aim is to make the students think as a fluid. In addition to relating a working knowledge of fluid mechanics, the subject prepares students for higher-level subjects in fluid dynamics.
This Project has been completed as part of a standard 10 weeks Calculus 3 asynchronous online course with optional WebEx sessions during Summer 2021 Semester at MassBay Community College, Wellesley Hills, MA.
This Project has been completed as part of a standard Calculus 3 in-person course with during Fall 2023 semester at MassBay Community College, Wellesley Hills, MA.
This Project has been completed as part of a standard 10 weeks Calculus 1 asynchronous online course with optional WebEx sessions during Summer 2021 Semester at MassBay Community College, Wellesley Hills, MA.
This Project has been completed as part of a standard 10 weeks Calculus 1 face to face course during Summer 2022 semester at MassBay Community College, Wellesley Hills, MA.
This open-source book by Crowell, Robbin, and Angenent is a spin-off of a previous open-source book by Robbin and Angenent. It covers the first semester of a freshman calculus course.
This Project has been completed as part of a standard 10 weeks Calculus 3 asynchronous online course with optional WebEx sessions during Summer 2021 Semester at MassBay Community College, Wellesley Hills, MA.
Highlights of Calculus is a series of short videos that introduces the basics of calculus—how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject. The series is divided into three sections:
Introduction
Why Professor Strang created these videos
How to use the materials
Highlights of Calculus
Five videos reviewing the key topics and ideas of calculus
Applications to real-life situations and problems
Additional summary slides and practice problems
Derivatives
Twelve videos focused on differential calculus
More applications to real-life situations and problems
Additional summary slides and practice problems
About the Instructor
Professor Gilbert Strang is a renowned mathematics professor who has taught at MIT since 1962. Read more about Prof. Strang.
Acknowledgements
Special thanks to Professor J.C. Nave for his help and advice on the development and recording of this program.
The video editing was funded by the Lord Foundation of Massachusetts.
This course focuses on an in-depth reading of Principia Mathematica Philosophiae Naturalis by Isaac Newton, as well as several related commentaries and historical philosophical texts.
With Applications to Biology and Environmental Science
Short Description:
This book is an approachable introduction to calculus with applications to biology and environmental science. For example, one application in the book is determining the volume of earth moved in the 1959 earthquake that created Quake Lake. Another application uses differential equations to model various biological examples, including moose and wolf populations at Isle Royale National Park, ranavirus in amphibians, and competing species of protozoa. The text focuses on intuitive understanding of concepts, but still covers most of the algebra and calculations common in a survey of calculus course.
Word Count: 37976
(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)
KiteModeler was developed in an effort to foster hands-on, inquiry-based learning in science and math. KiteModeler is a simulator that models the design, trimming, and flight of a kite. The program works in three modes: Design Mode, Trim Mode, or Flight Mode. In the Design Mode (shown below), you pick from five basic types of kite designs. You can then change design variables including the length and width of various sections of the kite. You can also select different materials for each component. When you have a design that you like, you switch to the Trim Mode where you set the length of the bridle string and tail and the location of the knot attaching the bridle to the control line. Based on your inputs, the program computes the center of gravity and pressure, the magnitude of the aerodynamic forces and the weight, and determines the stability of your kite. With a stable kite design, you are ready for Flight Mode. In Flight Mode you set the wind speed and the length of control line. The program then computes the sag of the line caused by the weight of the string and the height and distance that your kite would fly. Using all three modes, you can investigate how a kite flies, and the factors that affect its performance.
This Project has been completed as part of a standard 10 weeks Calculus 1 asynchronous online course with optional WebEx sessions during Summer 2021 Semester at MassBay Community College, Wellesley Hills, MA.
Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space.
MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology. Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication.
These notes are intended to provide a brief, noncomprehensive introduction to GNU Octave, a free open source alternative to MatLab. The basic syntax and usage is explained through concrete examples from the mathematics courses a math, computer science, or engineering major encounters in the first two years of college: linear algebra, calculus, and differential equations.
Our goal with this textbook is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.
The textbook contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds.
This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course.
The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calculus sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equation, also provide useful preparatory experience.) Chapters 6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5.
David Wolfe, Emeritus Professor of Physics, University of New Mexico, and Director, Oppenheimer Institute for Science and International Cooperation. Isaac Newton has a good claim to being the most famous man of the last 500 years. Whilst no individual can claim to be the originator of what has come to be called the Scientific Revolution, surely Isaac Newton is more responsible than any other single person. If we look at the technology on which our modern world is based - from the existence of electricity to transport to telecommunications and much else - all are based on the science which developed from the 18th century onwards. The Enlightenment, itself, and the concept of the individual, all developed as a result of his thinking. Even the reaction to these ideas from Romanticism to Fascism came about because of the rise of intellectual enquiry. Yet Newton does not fit the picture of 'the scientist' that we hold today. He spent more of his life thinking about alchemy and religion than he did about mathematics or physics. Moreover, he was one of history's greatest misanthropes. Left by his mother at three years of age, he appears never to have recovered from that trauma. This course will investigate Newton's life and work in relation to his achievements and also to his arguments with such people as Robert Hooke, John Flamsteed - the first Astronomer Royal, and Gottfried Leibniz- the codiscoverer of the calculus. An astounding genius, Newton was a deeply flawed human being.
This Project has been completed as part of a standard Calculus 3 synchronous online course during Fall 2020 Semester at MassBay Community College, Wellesley Hills, MA.