Students explore the properties of composites using inexpensive materials and processing techniques. They create beams using Laffy Taffy and water, and a choice of various reinforcements (pasta, rice, candies) and fabricating temperatures. Student groups compete for the highest strength beam. They measure flexure strength with three-point bend tests and calculations. Results are compared and discussed to learn how different materials and reinforcement shapes affect material properties and performance.

Biology is designed for multi-semester biology courses for science majors. It is grounded on an evolutionary basis and includes exciting features that highlight careers in the biological sciences and everyday applications of the concepts at hand. To meet the needs of today’s instructors and students, some content has been strategically condensed while maintaining the overall scope and coverage of traditional texts for this course. Instructors can customize the book, adapting it to the approach that works best in their classroom. Biology also includes an innovative art program that incorporates critical thinking and clicker questions to help students understand—and apply—key concepts.

By the end of this section, you will be able to:Describe epithelial tissuesDiscuss the different types of connective tissues in animalsDescribe three types of muscle tissuesDescribe nervous tissue

Students create and analyze composite materials with the intent of using the materials to construct a structure with optimal strength and minimal density. The composite materials are made of puffed rice cereal, marshmallows and chocolate chips. Student teams vary the concentrations of the three components to create their composite materials. They determine the material density and test its compressive strength by placing weights on it and measuring how much the material compresses. Students graph stress vs. strain and determine Young's modulus to analyze the strength of their materials.

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.

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.

This course is about the mathematics that is most widely used in the mechanical engineering core subjects: An introduction to linear algebra and ordinary differential equations (ODEs), including general numerical approaches to solving systems of equations.

This course is is a collection of resources on OER Commons curated for Adult Education instructors and students to show the integration of math into the Information Technology Career Sector. Students will analyze and practice specific skills related to being in IT as well as develop math skills. Modules in this curriculum guide can be studied in any particular order as one does not necessarily build upon the other. Each includes the idea of building mathematical and logic skills required for programming and other IT related careers.

This course was offered as a non-credit program during the Independent Activities Period (IAP), January 2008. A more recent version is available as course 18.S997 Introduction To MATLAB Programming, including video lectures.
The course, intended for students with no programming experience, provides the foundations of programming in MATLAB®. Variables, arrays, conditional statements, loops, functions, and plots are explained. At the end of the course, students should be able to use MATLAB in their own work, and be prepared to deepen their MATLAB programming skills and tackle other languages for computing, such as Java, C++, or Python.
The course mostly follows the official MATLAB Manual, available from The MathWorks. We will cover material from chapters 2-5.

Welcome to this online course on Linear Algebra.

Linear Algebra is a branch of mathematics that plays a fundamental to role in many parts of Science and Engineering, such as Quantum Mechanics, Coding Theory, Signal Processing and Control Theory .

As Linear Algebra is a common component of many university programmes in Science or Engineering, this course can be used as additional study or preparation for on campus courses on Linear Algebra. Please note that we cannot guarantee that this course can replace an on campus course.

The course has no preliminaries other than basic high school mathematics. Furthermore, the course is self contained; it can be studied without extra resources. Nevertheless, for each topic you can find some references to standard literature that you can consult for further reading.

This 12-minute video lesson provides another example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form. [Linear Algebra playlist: Lesson 32 of 143]

This course on global integration brings together matters of global markets and institutions, global strategy, organization, and leadership. Global integration, the process by which an organization with units around the world becomes united, will be presented as a link to entrepreneurship and general management. The seminar is offered only to those enrolled in the MIT Sloan Fellows Program and challenges the participants to draw upon their past managerial experiences, especially those affiliated with multinational companies.

This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis.

This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include Vectors and Matrices, Partial Derivatives, Double and Triple Integrals, and Vector Calculus in 2 and 3-space.

This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space.
MIT OpenCourseWare offers another version of 18.02, from the Spring 2006 term. Both versions cover the same material, although they are taught by different faculty and rely on different textbooks. Multivariable Calculus (18.02) is taught during the Fall and Spring terms at MIT, and is a required subject for all MIT undergraduates.

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.
The materials have been organized to support independent study. The website includes all of the materials you will need to understand the concepts covered in this subject. The materials in this course include:

Lecture Videos recorded on the MIT campus
Recitation Videos with problem-solving tips
Examples of solutions to sample problems
Problems for you to solve, with solutions
Exams with solutions
Interactive Java Applets (“Mathlets”) to reinforce key concepts

Content Development
Denis Auroux 
Arthur Mattuck 
Jeremy Orloff 
John Lewis
Heidi Burgiel 
Christine Breiner 
David Jordan 
Joel Lewis

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.
The materials have been organized to support independent study. The website includes all of the materials you will need to understand the concepts covered in this subject. The materials in this course include:

Lecture Videos recorded on the MIT campus
Recitation Videos with problem-solving tips
Examples of solutions to sample problems
Problems for you to solve, with solutions
Exams with solutions
Interactive Java Applets (“Mathlets”) to reinforce key concepts

Content Development
Denis Auroux 
Arthur Mattuck 
Jeremy Orloff 
John Lewis
Heidi Burgiel 
Christine Breiner 
David Jordan 
Joel Lewis

This site teaches Vector and Matrix Quantities to High Schoolers through a series of 2195 questions and interactive activities aligned to 16 Common Core mathematics skills.

The goal of this course is to illustrate the spectroscopy of small molecules in the gas phase: quantum mechanical effective Hamiltonian models for rotational, vibrational, and electronic structure; transition selection rules and relative intensities; diagnostic patterns and experimental methods for the assignment of non-textbook spectra; breakdown of the Born-Oppenheimer approximation (spectroscopic perturbations); the stationary phase approximation; nondegenerate and quasidegenerate perturbation theory (van Vleck transformation); qualitative molecular orbital theory (Walsh diagrams); the notation of atomic and molecular spectroscopy.