Linear algebra, vector space methods, and functional analysis are a powerful setting for many topics in engineering, science (including social sciences), and business. This collection starts with the simple idea of a matrix times a vector and develops tools and interpretations for many signal processing and system analysis and design methods.
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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.
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.
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.
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.
One can look at the operation of a matrix times a vector as changing the basis set for the vector or as changing the vector with the same basis description.
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 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. Users may find additional or updated materials at Professor Carter's 3.016 course Web site.
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.
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."
Evidence Choice Matrix
VA:Pr6.1.HSI - Analyze and describe the impact that an exhibition or collection has on personal awareness of social, cultural, or political beliefs and understandings.
This matrix can be used to provide students with some options as to the ways in which they can provide evidence of learning toward a grade level standard in art.