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.
Subject:
Business, Mathematics and Statistics, Science and Technology, Social Sciences
Principles of materials science and cell biology underlying the design of medical implants, artificial organs, and matrices for tissue engineering. Methods for biomaterials surface characterization and analysis of protein adsorption on biomaterials. Molecular and cellular interactions with biomaterials are analyzed in terms of unit cell processes, such as matrix synthesis, degradation, and contraction. Mechanisms underlying wound healing and tissue remodeling following implantation in various organs. Tissue and organ regeneration. Design of implants and prostheses based on control of biomaterials-tissue interactions. Comparative analysis of intact, biodegradable, and bioreplaceable implants by reference to case studies. Criteria for restoration of physiological function for tissues and organs.
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.
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.
Subject:
Business, Mathematics and Statistics, Science and Technology, Social Sciences
A short introduction to writing Content MathML by hand. It covers tokens, prefix notation, and applying functions and operators. In addition it introduces writing derivatives, integrals, vectors, and matrices.
Subject:
Mathematics and Statistics, Science and Technology
The main purpose of our device is to detect velocity of motions in a movie file, and it is helpful to understand the mechanism in idealized cases. It is too complicated to come up with appropriate algorithms for all possible input data at once, and we want to look at the simplest cases first. Our choice of data is a simulated movie. Reducing to bare bones, a blank, constant background (noise-free) with a single object moving across the screen is a good start.
This course offers a rigorous treatment of linear algebra, including vector spaces, systems of linear equations, bases, linear independence, matrices, determinants, eigenvalues, inner products, quadratic forms, and canonical forms of matrices. Compared with Linear Algebra (18.06), more emphasis is placed on theory and proofs.
Overview of the use of a matrix times a vector for the description of signal and systems operations. The vectors are descriptions of the signals and the matrix operator is a description of the system.
Subject:
Business, Mathematics and Statistics, Science and Technology, Social Sciences
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.
Subject:
Mathematics and Statistics, Science and Technology
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